AFOQT · Practice test

Free AFOQT practice test

165 questions: fifteen from each of the eleven subtests, the right answer after every question, with no account and no clock.

Verbal Analogies

15 questions

  1. Item 1 of 15

    professor is to campus as ___

    1. editor is to deadline
    2. merchant is to customer
    3. clerk is to receipt
    4. architect is to compass
    5. banker is to branch
    Show the answer

    Answer: banker is to branch

    A professor works on a campus, and a banker works at a branch: a worker and the place of the work.

    A deadline is a time limit, a compass a drafting tool and a receipt a slip handed over, none of them a place.

    A customer is the person a merchant serves, not where the merchant works.

  2. Item 2 of 15

    hourglass is to measure as ___

    1. delay is to frustrate
    2. clock is to tick
    3. pendulum is to swing
    4. athlete is to sprint
    5. alarm is to awaken
    Show the answer

    Answer: alarm is to awaken

    An hourglass exists to measure time, and an alarm exists to awaken a sleeper: a device and its purpose.

    A clock ticks and a pendulum swings, but a sound or a motion is not the job the device was made for.

    An athlete is a person, not a device, and a delay is an event that may frustrate.

  3. Item 3 of 15

    day is to month as step is to ___

    1. ramp
    2. elevator
    3. catwalk
    4. trapdoor
    5. stairway
    Show the answer

    Answer: stairway

    A day is one part of a month, and a step is one part of a stairway: a part and its whole.

    A ramp is a smooth slope and an elevator a moving car, neither one built of steps.

    A catwalk is a level walkway, and a trapdoor is an opening in a floor or ceiling.

  4. Item 4 of 15

    top is to bottom as ___

    1. racer is to speedy
    2. shoelace is to tie
    3. poke is to jab
    4. eyebrow is to eyelash
    5. fast is to slow
    Show the answer

    Answer: fast is to slow

    Top and bottom are opposites, and so are fast and slow.

    Poke is to jab is a change of degree, and eyebrow is to eyelash names two neighbors.

    A racer is known for being speedy and a shoelace is made to tie: a trait and a use, not opposites.

  5. Item 5 of 15

    smoke is to coughing as glare is to ___

    1. sweating
    2. yawning
    3. shivering
    4. sneezing
    5. squinting
    Show the answer

    Answer: squinting

    Smoke brings on coughing, and glare brings on squinting: an irritant and the reaction of the body to it.

    Sweating is the reaction to heat, and shivering is the reaction to cold.

    Sneezing answers dust or pollen, and yawning answers drowsiness, not bright light.

  6. Item 6 of 15

    anorak is to outerwear as ___

    1. puppy is to chew
    2. breed is to poodle
    3. doghouse is to yard
    4. leash is to walk
    5. beagle is to hound
    Show the answer

    Answer: beagle is to hound

    An anorak is one kind of outerwear, and a beagle is one kind of hound: a member and its category.

    Breed is to poodle reverses the order, naming the category before the member.

    A puppy chews, a leash is for walking and a doghouse sits in a yard: a habit, a use and a place.

  7. Item 7 of 15

    poker is to stoke as defroster is to ___

    1. refrigerate
    2. humidify
    3. douse
    4. light
    5. unfreeze
    Show the answer

    Answer: unfreeze

    A poker is used to stoke a fire, and a defroster is used to unfreeze a frosted window: a tool and its job.

    Refrigerate is the job of a fridge, and humidify is the job of a humidifier.

    Douse and light act on a fire, which belongs to the poker half of the analogy.

  8. Item 8 of 15

    overuse is to wear as sunlight is to ___

    1. fading
    2. rusting
    3. denting
    4. gloom
    5. tarnishing
    Show the answer

    Answer: fading

    Overuse causes wear, and sunlight causes fading: an agent and the mark it leaves.

    Rusting comes from damp, tarnishing from the air and denting from a blow, all other causes.

    Gloom comes from the absence of sunlight, the opposite condition.

  9. Item 9 of 15

    asset is to liability as ___

    1. salary is to income
    2. splurge is to debt
    3. consensus is to accord
    4. harmony is to discord
    5. duet is to trio
    Show the answer

    Answer: harmony is to discord

    An asset is value owned and a liability is a debt owed, two opposites, like harmony and discord.

    Consensus and accord are synonyms, and a salary is one kind of income.

    A splurge can lead to debt, and a duet and a trio differ in number, not in sense.

  10. Item 10 of 15

    increase is to decrease as naive is to ___

    1. gullible
    2. earnest
    3. childish
    4. worldly
    5. bookish
    Show the answer

    Answer: worldly

    Decrease is the opposite of increase, and worldly, wise in the ways of life, is the opposite of naive.

    Gullible and childish lean the same way as naive, near-synonyms rather than opposites.

    Earnest and bookish name separate traits that a naive person may well share.

  11. Item 11 of 15

    provocation is to retaliation as generosity is to ___

    1. greed
    2. charity
    3. jealousy
    4. thankfulness
    5. stinginess
    Show the answer

    Answer: thankfulness

    A provocation draws retaliation in return, and generosity draws thankfulness: an act and the response it earns.

    Stinginess is the opposite of generosity, and charity is generosity itself, not a response to it.

    Greed is a wish to keep more, and jealousy answers the good fortune of another, not a gift.

  12. Item 12 of 15

    tine is to fork as ___

    1. grater is to shredder
    2. ladle is to soup
    3. drawer is to knob
    4. corkscrew is to bottle
    5. rung is to ladder
    Show the answer

    Answer: rung is to ladder

    A tine is one of the prongs of a fork, and a rung is one of the steps of a ladder: a part and its whole.

    Drawer is to knob runs the other way, naming the whole before the part.

    A grater and a shredder are related tools, and a corkscrew and a ladle pair a tool with what it opens or serves.

  13. Item 13 of 15

    acquit is to convict as ratify is to ___

    1. negotiate
    2. circulate
    3. repudiate
    4. implement
    5. endorse
    Show the answer

    Answer: repudiate

    To acquit and to convict are opposite verdicts, and to ratify and to repudiate are opposite answers to a treaty.

    Endorse means much the same as ratify, a near-synonym rather than an opposite.

    Negotiate comes before ratifying, implement comes after it and circulate takes no side.

  14. Item 14 of 15

    cramped is to spacious as ___

    1. skimpy is to bountiful
    2. hungry is to ravenous
    3. simmered is to tender
    4. filling is to hearty
    5. morsel is to meal
    Show the answer

    Answer: skimpy is to bountiful

    Cramped and spacious are opposite ends of one scale, and so are skimpy and bountiful.

    Hungry is to ravenous is a change of degree, and filling and hearty mean nearly the same.

    A morsel is a small part of a meal, and simmering is the cooking that leaves meat tender.

  15. Item 15 of 15

    placid is to tranquil as ___

    1. anxious is to nervous
    2. worried is to petrified
    3. serene is to hysterical
    4. delighted is to content
    5. startled is to jumpy
    Show the answer

    Answer: anxious is to nervous

    Placid and tranquil name the same calm at the same strength, and anxious and nervous name the same unease.

    Worried is to petrified rises in degree, and delighted is to content falls in degree.

    Serene and hysterical are opposites, and startled is to jumpy ties a sudden fright to the edgy state that follows.

Arithmetic Reasoning

15 questions

  1. Item 1 of 15

    A body shop quotes a repair at $960 and asks for a deposit of 40% of the quote before the work starts. How large is the deposit?

    1. $400.00
    2. $1,344.00
    3. $576.00
    4. $384.00
    5. $920.00
    Show the answer

    Answer: $384.00

    The deposit is 40% of the quote: 0.40 × $960 = $384.00.

    $576.00 is the 60% still owed, and $1,344.00 adds the deposit to the quote.

    $920.00 takes $40 off the quote, and $400.00 takes 40% of $1,000.

  2. Item 2 of 15

    A survey boat and a smaller boat leave a marker buoy and travel in opposite directions. Over the next 5 hours the survey boat covers 76 miles and the smaller boat covers 52 miles. How far apart are the two boats when those 5 hours are up, in miles?

    1. 204
    2. 128
    3. 133
    4. 125
    5. 180
    Show the answer

    Answer: 128

    The boats move apart, so their runs add up: 76 + 52 = 128 miles.

    204 and 180 add one boat's run a second time.

    133 adds the 5 hours to the 128 miles.

  3. Item 3 of 15

    A landscaping company spreads 9 cubic yards of topsoil on each lawn it renovates. This season's delivery is 180 cubic yards, and the company runs 6 renovation crews. How many lawns will the season's topsoil cover?

    1. 30
    2. 20
    3. 12
    4. 60
    5. 26
    Show the answer

    Answer: 20

    Each lawn takes 9 cubic yards, so the delivery covers 180 ÷ 9 = 20 lawns.

    30 divides by the 6 crews, a detail the question does not need.

    12 divides by 9 + 6, and 26 adds the 6 crews to the 20 lawns.

  4. Item 4 of 15

    A lumberyard charges 4% in sales tax on everything it sells over the counter. One crate of floor tile carries a shelf price of $150 before that tax. How much does a customer hand over for the crate?

    1. $157.50
    2. $144.00
    3. $162.24
    4. $154.00
    5. $156.00
    Show the answer

    Answer: $156.00

    The tax is 0.04 × $150 = $6.00, so the customer pays $150 + $6.00 = $156.00.

    $144.00 subtracts the tax, and $157.50 uses 5% instead of 4%.

    $154.00 adds $4 instead of 4%, and $162.24 charges the tax twice.

  5. Item 5 of 15

    A distributor unloads 120 crates of fruit, and 3/10 of the crates hold limes. How many crates hold limes?

    1. 15
    2. 40
    3. 12
    4. 30
    5. 36
    Show the answer

    Answer: 36

    One tenth of 120 is 12 crates, so three tenths is 3 × 12 = 36.

    12 stops at one tenth, and 40 divides by 3 instead of taking 3/10.

    30 takes a quarter of the crates instead of three tenths.

  6. Item 6 of 15

    A tool chest holds 6 cubic feet. A workshop keeps 18 of them and has 8 more of the same size on order. How many cubic feet will all the chests hold once the order arrives?

    1. 108
    2. 116
    3. 66
    4. 156
    5. 168
    Show the answer

    Answer: 156

    After the order there are 18 + 8 = 26 chests, holding 26 × 6 = 156 cubic feet.

    108 counts only the 18 chests on hand, and 66 multiplies only the 8 on order.

    116 adds the 8 chests to 108 as if they were cubic feet.

  7. Item 7 of 15

    An inspector checked 1,250 pipe fittings in a first batch, passed 1,175 of them and set the rest aside. A second batch the next day held 1,000 fittings. What percent of the fittings in the first batch were set aside?

    1. 7.5%
    2. 3.3%
    3. 5.8%
    4. 6.4%
    5. 6.0%
    Show the answer

    Answer: 6.0%

    1,250 − 1,175 = 75 fittings were set aside, and 75 ÷ 1,250 = 0.06, or 6.0%.

    7.5% divides by the second batch of 1,000, and 6.4% divides by the 1,175 passed.

    3.3% divides by both batches together, 2,250.

  8. Item 8 of 15

    One filling line fills 1,750 jars per hour. With a second line running alongside, the two lines fill 30,800 jars in 7 hours. How many jars per hour does the second line fill?

    1. 4,400
    2. 6,150
    3. 2,650
    4. 2,200
    5. 4,150
    Show the answer

    Answer: 2,650

    Together the lines fill 30,800 ÷ 7 = 4,400 jars an hour, so the second fills 4,400 − 1,750 = 2,650.

    4,400 is the two lines together, and 6,150 adds the first line to that total.

    2,200 splits the total evenly between two lines that run at different rates.

  9. Item 9 of 15

    The minute hand of a large clock is 8 inches long and its tip reaches the rim of the face, going all the way around once an hour. Use 3.14 for pi. How many inches does the tip travel in 3 hours?

    1. 53.24
    2. 75.36
    3. 48.00
    4. 188.40
    5. 150.72
    Show the answer

    Answer: 150.72

    One turn is 2 × 3.14 × 8 = 50.24 inches, so 3 hours give 50.24 × 3 = 150.72.

    75.36 forgets to double the radius, and 48.00 leaves pi out: 2 × 8 × 3.

    53.24 adds the 3 hours to one turn instead of multiplying.

  10. Item 10 of 15

    A caterer fills 15 pitchers with punch, and each pitcher holds 3 quarts. How many pints of punch does the caterer pour?

    1. 45
    2. 30
    3. 90
    4. 47
    5. 36
    Show the answer

    Answer: 90

    The pitchers hold 15 × 3 = 45 quarts, and at 2 pints a quart that is 45 × 2 = 90 pints.

    45 stops at quarts, and 47 adds 2 instead of multiplying by 2.

    30 doubles the 15 pitchers and leaves out the 3 quarts each.

  11. Item 11 of 15

    A maintenance crew of 24 workers makes up 30% of a plant's staff. The plant then grows its staff by 25%, all hired outside the crew. How many workers are not on the crew?

    1. 76
    2. 56
    3. 100
    4. 64
    5. 81
    Show the answer

    Answer: 76

    The staff is 24 ÷ 0.30 = 80, then 80 × 1.25 = 100, so 100 − 24 = 76 are not on the crew.

    56 is 80 − 24, the count before the hiring.

    100 is the whole staff, crew included.

  12. Item 12 of 15

    A 14-ounce canister of oats costs $2.80, and a 21-ounce canister costs $3.57. A kitchen needs 42 ounces. How much is saved over the whole 42 ounces by buying the 21-ounce canisters instead of the 14-ounce ones?

    1. $0.77
    2. $1.89
    3. $0.42
    4. $1.54
    5. $1.26
    Show the answer

    Answer: $1.26

    42 ounces cost 3 × $2.80 = $8.40 in small canisters and 2 × $3.57 = $7.14 in large ones: $1.26 saved.

    $0.77 is the gap between one canister of each size, and $1.54 doubles that gap.

    $0.42 applies the $0.03 gap per ounce to 14 ounces instead of 42.

  13. Item 13 of 15

    A car running at a steady 78 miles per hour is 39 miles behind a tanker that runs at a steady 52 miles per hour on the same highway. How many minutes does the car need to pull alongside?

    1. 18
    2. 110
    3. 45
    4. 90
    5. 30
    Show the answer

    Answer: 90

    The car closes 78 − 52 = 26 miles an hour, so 39 ÷ 26 = 1.5 hours, or 90 minutes.

    30 ignores the tanker's speed (39 ÷ 78), and 45 uses the tanker's speed alone (39 ÷ 52).

    18 adds the speeds, 39 ÷ 130, as if the vehicles were driving toward each other.

  14. Item 14 of 15

    A supply room's order holds 48 items, half of them clipboards and half staplers, and comes to $408. A clipboard costs $10. What does one stapler cost?

    1. $16.80
    2. $8.50
    3. $17.00
    4. $7.00
    5. $3.50
    Show the answer

    Answer: $7.00

    24 clipboards cost 24 × $10 = $240, leaving $408 − $240 = $168 for 24 staplers: $7.00 each.

    $17.00 charges the whole $408 to the staplers, and $8.50 is the average price of all 48 items.

    $3.50 divides the staplers' $168 by all 48 items, and $16.80 divides it by the clipboard's $10.

  15. Item 15 of 15

    A delivery van drives 4 hours at 30 miles per hour, then continues at 50 miles per hour. Over the whole drive the van averages 42 miles per hour. How many miles does the van cover at 50 miles per hour?

    1. 300
    2. 420
    3. 120
    4. 500
    5. 168
    Show the answer

    Answer: 300

    If the drive lasts t hours, 42t = 120 + 50(t − 4), so t = 10 and the second leg is 6 × 50 = 300 miles.

    420 is the whole drive, 42 × 10, and 500 runs all 10 hours at 50.

    120 is the first leg, and 168 is 42 × 4.

Word Knowledge

15 questions

  1. Item 1 of 15

    ASPECT most nearly means

    1. purpose
    2. emphasis
    3. context
    4. feature
    5. timing
    Show the answer

    Answer: feature

    An aspect is one distinct side or part of a thing, so the closest word is feature.

    A purpose is the reason for a thing, and an emphasis is the extra weight placed on one part.

    Context is the setting around a thing, and timing is when it happens.

  2. Item 2 of 15

    SCHOLAR most nearly means

    1. author
    2. librarian
    3. academic
    4. pioneer
    5. collector
    Show the answer

    Answer: academic

    A scholar is a learned person who studies a subject in depth, so the closest word is academic.

    An author writes books and a librarian runs a library: jobs, not depth of learning.

    A pioneer leads the way into new ground, and a collector gathers objects of one kind.

  3. Item 3 of 15

    PRAISE most nearly means

    1. encourage
    2. compliment
    3. tutor
    4. hire
    5. nominate
    Show the answer

    Answer: compliment

    To praise is to express approval or admiration, so the closest word is compliment.

    Encourage is a near-miss: it means to give support or hope, not to voice admiration.

    Tutor means to teach, hire means to give a job and nominate means to propose for an office or award.

  4. Item 4 of 15

    SLUMBER most nearly means

    1. daydream
    2. stretch
    3. stroll
    4. whisper
    5. sleep
    Show the answer

    Answer: sleep

    To slumber is to sleep, so the closest word is sleep.

    Daydream means to let the mind drift while awake, and stretch means to extend the limbs.

    Stroll means to walk slowly, and whisper means to speak very softly.

  5. Item 5 of 15

    WRECK most nearly means

    1. destroy
    2. abandon
    3. stain
    4. bend
    5. tow
    Show the answer

    Answer: destroy

    To wreck something is to damage it beyond use, so the closest word is destroy.

    Stain and bend name lesser damage: a mark left behind, a shape forced out of line.

    Abandon means to leave behind, and tow means to pull a vehicle behind another.

  6. Item 6 of 15

    ORCHESTRATE most nearly means

    1. commission
    2. broadcast
    3. mastermind
    4. premiere
    5. bankroll
    Show the answer

    Answer: mastermind

    To orchestrate a plan is to arrange and direct it, often from behind the scenes, so the closest word is mastermind.

    Commission means to order a work from someone, and bankroll means to pay for it.

    Broadcast means to send out over radio or television, and premiere means to present for the first time.

  7. Item 7 of 15

    CHARISMATIC most nearly means

    1. magnetic
    2. intense
    3. overbearing
    4. robotic
    5. upbeat
    Show the answer

    Answer: magnetic

    A charismatic person has a charm that draws others in, so the closest word is magnetic.

    Upbeat is a near-miss: it means cheerful, a mood rather than a pull on others.

    Intense means showing strong focus, overbearing means domineering and robotic means stiff and cold.

  8. Item 8 of 15

    INTERACT most nearly means

    1. tease
    2. favor
    3. compete
    4. negotiate
    5. communicate
    Show the answer

    Answer: communicate

    To interact is to deal with others back and forth, so the closest word is communicate.

    Negotiate is a near-miss: it is talk aimed at reaching an agreement, a narrower act.

    Tease means to make playful fun, favor means to prefer one thing and compete means to strive against others.

  9. Item 9 of 15

    APT most nearly means

    1. pressing
    2. cheery
    3. fitting
    4. proud
    5. bold
    Show the answer

    Answer: fitting

    An apt remark is exactly suited to the occasion, so the closest word is fitting.

    Pressing means urgent, and cheery means bright and good-humored.

    Proud means pleased with one's own standing, and bold means daring.

  10. Item 10 of 15

    MARGINAL most nearly means

    1. lopsided
    2. wobbly
    3. outward
    4. sporadic
    5. slight
    Show the answer

    Answer: slight

    Marginal means small in amount or importance, as in a marginal gain, so the closest word is slight.

    Outward is a near-miss on margin as an edge: it means on the outside, not small.

    Lopsided means uneven, wobbly means unsteady and sporadic means happening now and then.

  11. Item 11 of 15

    INSIPID most nearly means

    1. coarse
    2. brief
    3. bland
    4. greasy
    5. elaborate
    Show the answer

    Answer: bland

    Something insipid lacks flavor and interest, so the closest word is bland.

    Coarse means rough in texture, and greasy means heavy with oil or fat.

    Brief means short in time, and elaborate means worked out in rich detail, nearly the opposite.

  12. Item 12 of 15

    NEBULOUS most nearly means

    1. scattered
    2. vague
    3. complicated
    4. lengthy
    5. poetic
    Show the answer

    Answer: vague

    Nebulous means hazy and ill-defined, so the closest word is vague.

    Scattered is a near-miss: it means spread out without order, not unclear in meaning.

    Complicated means made of many tangled parts, lengthy means long and poetic means written like verse.

  13. Item 13 of 15

    URBANE most nearly means

    1. polished
    2. reclusive
    3. homely
    4. hearty
    5. diffident
    Show the answer

    Answer: polished

    An urbane person has smooth, refined manners, so the closest word is polished.

    Homely means plain and unrefined, and reclusive means avoiding company, both close to the opposite.

    Hearty means warm and loudly enthusiastic, and diffident means shy and unsure.

  14. Item 14 of 15

    CORPULENT most nearly means

    1. plump
    2. brawny
    3. towering
    4. hunched
    5. bald
    Show the answer

    Answer: plump

    Corpulent describes a large, heavy body, so the closest word is plump.

    Brawny is a near-miss: it means big through muscle, not through fat.

    Towering means very tall, hunched means bent forward and bald means without hair.

  15. Item 15 of 15

    PARTISAN most nearly means

    1. candidate
    2. supporter
    3. voter
    4. organizer
    5. observer
    Show the answer

    Answer: supporter

    A partisan is a strong, often biased supporter of a party or cause, so the closest word is supporter.

    A voter casts a ballot and an organizer arranges a group, neither one necessarily devoted to a side.

    A candidate seeks office, and an observer watches without taking part.

Math Knowledge

15 questions

  1. Item 1 of 15

    When a = 4 and b = 9, 2a + 3b =

    1. 35
    2. 30
    3. 13
    4. 17
    5. 20
    Show the answer

    Answer: 35

    2a + 3b = 2(4) + 3(9) = 8 + 27 = 35.

    30 swaps the coefficients, 3(4) + 2(9), and 17 doubles a but does not triple b: 8 + 9.

    13 only adds a and b, and 20 multiplies 2 + 3 by a alone, leaving b out.

  2. Item 2 of 15

    Two angles are supplementary and one measures 110°. The other, in degrees, measures

    1. 20
    2. 180
    3. 110
    4. 70
    5. 290
    Show the answer

    Answer: 70

    Supplementary angles add up to 180°, so the other angle is 180° − 110° = 70°.

    20 subtracts 90 instead, as for complementary angles, and 290 adds 110 to 180.

    180 is the total of the pair, and 110 repeats the angle given.

  3. Item 3 of 15

    Which of these is a prime number?

    1. 27
    2. 25
    3. 17
    4. 21
    5. 33
    Show the answer

    Answer: 17

    17 has no divisors other than 1 and itself, so it is prime.

    21 = 3 × 7, 27 = 3 × 3 × 3 and 33 = 3 × 11, all multiples of 3.

    25 = 5 × 5, so it is not prime either.

  4. Item 4 of 15

    The solution of 7x = 3.5 is

    1. 24.5
    2. 10.5
    3. 2.0
    4. 0.05
    5. 0.5
    Show the answer

    Answer: 0.5

    Dividing both sides by 7 gives x = 3.5 ÷ 7 = 0.5.

    24.5 multiplies by 7 instead of dividing, and 2.0 divides 7 by 3.5, the wrong way round.

    10.5 adds 7 to 3.5, and 0.05 misplaces the decimal point.

  5. Item 5 of 15

    (5 × 2)³ =

    1. 1000
    2. 30
    3. 125
    4. 500
    5. 8
    Show the answer

    Answer: 1000

    5 × 2 = 10 and 10³ = 1000; the same comes from 5³ × 2³ = 125 × 8.

    30 multiplies 10 by 3 instead of cubing it, and 500 squares the 2 instead of cubing it.

    125 and 8 cube only one of the two factors.

  6. Item 6 of 15

    9³ / 9³ =

    1. 9⁹
    2. 9
    3. 0
    4. 9⁶
    5. 1
    Show the answer

    Answer: 1

    A nonzero number divided by itself is 1; by the exponent rules, 9³ / 9³ = 9³⁻³ = 9⁰ = 1.

    9⁶ adds the exponents and 9⁹ multiplies them, but dividing subtracts them.

    0 confuses 9³ − 9³ with 9³ / 9³, and 9 treats the result as 9¹.

  7. Item 7 of 15

    A triangle has a base of 10 inches and a height of 6 inches. Its area, in square inches, is

    1. 16
    2. 60
    3. 20
    4. 10
    5. 30
    Show the answer

    Answer: 30

    The area of a triangle is (base × height) ÷ 2 = (10 × 6) ÷ 2 = 30 square inches.

    60 forgets to halve the product, giving the area of a rectangle, and 16 adds base and height.

    20 divides the product by 3 instead of 2, and 10 repeats the base.

  8. Item 8 of 15

    If x² − x − 42 = 0 and x < 0, then x =

    1. −3
    2. 42
    3. 6
    4. 1
    5. −6
    Show the answer

    Answer: −6

    x² − x − 42 factors as (x − 7)(x + 6), so x = 7 or x = −6, and only −6 is negative.

    6 has the wrong sign: 6² − 6 − 42 = −12, not 0.

    42 and 1 are not negative, and −3 gives 9 + 3 − 42 = −30, not 0.

  9. Item 9 of 15

    If 5 − 2x = −3, then x =

    1. −4
    2. 1
    3. −1
    4. 4
    5. 8
    Show the answer

    Answer: 4

    Subtracting 5 from both sides gives −2x = −8, and dividing by −2 gives x = 4.

    −4 loses the sign when dividing by −2, and 8 stops before dividing by 2.

    1 and −1 add 5 to −3 instead of subtracting it, which gives −2x = 2.

  10. Item 10 of 15

    √(20/5) + √(9 × 4) =

    1. 10
    2. 8
    3. 14
    4. 40
    5. 38
    Show the answer

    Answer: 8

    20/5 = 4 and √4 = 2; 9 × 4 = 36 and √36 = 6; so the sum is 2 + 6 = 8.

    40 adds 4 and 36 without taking either root, 38 roots only the first and 10 roots only the second.

    14 takes the root of the 9 alone: 2 + 3 × 4.

  11. Item 11 of 15

    Factor: 2x² + 5x + 3

    1. (2x − 1)(x + 3)
    2. (2x − 3)(x − 1)
    3. (2x + 1)(x + 3)
    4. (2x + 3)(x + 1)
    5. (2x + 3)(x − 1)
    Show the answer

    Answer: (2x + 3)(x + 1)

    (2x + 3)(x + 1) = 2x² + 2x + 3x + 3 = 2x² + 5x + 3.

    (2x + 1)(x + 3) gives a middle term of 7x, and (2x − 3)(x − 1) gives −5x.

    (2x − 1)(x + 3) and (2x + 3)(x − 1) both end in −3, not +3.

  12. Item 12 of 15

    If 4x + y = 14 and 2x + 3y = 12, then x + y =

    1. 3
    2. 5
    3. 2
    4. 1
    5. 26
    Show the answer

    Answer: 5

    y = 14 − 4x, so 2x + 3(14 − 4x) = 12 gives −10x = −30: x = 3, y = 2 and x + y = 5.

    3 is x alone, 2 is y alone and 1 is x − y.

    26 adds the two right-hand sides, 14 + 12, which gives 6x + 4y, not x + y.

  13. Item 13 of 15

    If S = 2πr² + 2πrh, then h =

    1. (S − 2πr)/(2πr²)
    2. (S + 2πr²)/(2πr)
    3. (S − 2πr²)/(2πr)
    4. 2πr/(S − 2πr²)
    5. S/(2πr)
    Show the answer

    Answer: (S − 2πr²)/(2πr)

    Subtracting 2πr² from both sides gives S − 2πr² = 2πrh, and dividing by 2πr gives h = (S − 2πr²)/(2πr).

    (S + 2πr²)/(2πr) adds the term instead of subtracting it, and S/(2πr) never removes it.

    2πr/(S − 2πr²) turns the fraction upside down, and (S − 2πr)/(2πr²) swaps 2πr and 2πr².

  14. Item 14 of 15

    If 5 − 2x ≥ 4x − 13, what is the greatest integer value of x?

    1. −2
    2. 2
    3. 3
    4. 1
    5. −3
    Show the answer

    Answer: 3

    Adding 2x and 13 to both sides gives 18 ≥ 6x, so x ≤ 3, and 3 itself is allowed.

    2 treats the inequality as strict, x < 3, though the sign allows equality.

    1, −2 and −3 also satisfy the inequality but are smaller than 3.

  15. Item 15 of 15

    Simplify: 3/4 ÷ (1/3 + 1/6) × 4/5

    1. 32/15
    2. 23/10
    3. 6/5
    4. 3/2
    5. 1/2
    Show the answer

    Answer: 6/5

    1/3 + 1/6 = 1/2 comes first; 3/4 ÷ 1/2 = 3/4 × 2 = 3/2; then 3/2 × 4/5 = 6/5.

    3/2 stops before the last step, 23/10 adds 4/5 instead of multiplying and 1/2 is the bracket alone.

    32/15 flips 3/4 instead of the divisor: 4/3 × 2 × 4/5.

Reading Comprehension

15 questions

  1. Item 1 of 15

    Spoilage is the work of bacteria, molds and yeasts, and each of them needs liquid water to grow, so the oldest methods of preservation are attempts to deny them that water rather than to poison them. Salting and sugaring exploit osmosis, the tendency of water to move across a cell membrane toward the side holding more dissolved material, which draws moisture out of the microbes and out of the food until the surface can no longer support life. Drying reaches the same end by removing the water outright, and a hard sausage or a dried apricot is safe for reasons that have nothing to do with temperature. Chemists express the idea as water activity, a measure of how much of the water present is free to take part in reactions rather than bound to salt, sugar or protein. Refrigeration proceeds on a different principle, leaving the water where it is and slowing every chemical and biological process instead, which postpones spoilage without arresting it. Freezing goes further, since water locked into ice is as unavailable to a microbe as water bound to salt. That is why a cured ham keeps on a shelf while a fresh one does not, and why the two demand different handling once the package has been opened.

    According to the passage, what makes a dried apricot safe to keep?

    1. The sugar in the fruit poisons the organisms that would spoil it
    2. The heat used in drying the fruit destroyed the microbes on it
    3. What such organisms need in order to grow has been taken out of the fruit
    4. The skin of the fruit keeps bacteria, molds and yeasts from the flesh
    Show the answer

    Answer: What such organisms need in order to grow has been taken out of the fruit

    Drying removes the water outright, and liquid water is what bacteria, molds and yeasts need in order to grow.

    The passage says the old methods deny microbes water rather than poison them, so the fruit's sugar is no poison here.

    A dried apricot is safe for reasons that have nothing to do with temperature, and the fruit's skin is never mentioned.

  2. Item 2 of 15

    Whether a world keeps an atmosphere is settled by a contest between the speed of its gas molecules and the speed required to escape its gravity. Molecules in a gas do not all travel at one speed but occupy a broad distribution, and raising the temperature shifts that whole distribution toward higher speeds. At any given temperature the lighter molecules travel fastest, so hydrogen and helium reach escape speed while nitrogen and carbon dioxide, many times heavier, lag behind. Escape speed in turn depends on the mass of a body and on how tightly that mass is packed, which is why a small world holds nothing for long while a giant one retains even the lightest gases. The loss is gradual rather than sudden, since only the fastest molecules of the distribution reach escape speed at any moment, and collisions among the remainder keep refilling the fast end of the distribution. Earth illustrates both outcomes at once, holding nitrogen and oxygen indefinitely while leaking hydrogen and helium into space. Low temperature can compensate for feeble gravity as well, which is how Titan, a moon whose surface gravity is a small fraction of Earth's, maintains a thick nitrogen atmosphere: its air is cold enough that the molecules move sluggishly.

    According to the passage, why is the loss of an atmosphere gradual rather than sudden?

    1. Because gravity strengthens as a planet sheds part of its atmosphere
    2. Because only the fastest molecules are moving quickly enough to break away
    3. Because collisions bring every molecule toward one common speed
    4. Because heavier gases settle into layers that shelter the lighter ones
    Show the answer

    Answer: Because only the fastest molecules are moving quickly enough to break away

    Only the fastest molecules of the distribution reach escape speed at any moment, so the loss is gradual.

    Gravity depends on a body's mass and how tightly it is packed, and nothing says it strengthens as gas leaves.

    Collisions refill the fast end rather than bring molecules to one speed, and no sheltering layers are described.

  3. Item 3 of 15

    James Madison came to the Bill of Rights as a reluctant convert. In 1788 he wrote to Thomas Jefferson that written guarantees were parchment barriers that determined majorities in the states had repeatedly overrun, and like other Federalists he held that a government of enumerated powers had no authority to invade such rights in the first place. Political circumstance altered his calculation, since he had promised voters in his race for a Virginia seat in the House to support amendments, and he believed that a modest set of protections would disarm opponents who were pressing for a second convention to reopen the whole document. In June 1789 he laid his proposals before the House of Representatives, intending that they be woven into the body of the Constitution at the places where each subject arose. The House chose instead to attach them as a separate list at the end of the document, a form urged by Roger Sherman among others, which is why the amendments stand apart from the original text today. Congress sent twelve amendments to the states in September 1789, and ten of them were ratified by December 1791. One of the remaining two, which delays any change in the pay of members of Congress until an election has intervened, was ratified in 1992 as the Twenty-seventh Amendment.

    According to the passage, how did Madison want his amendments added to the Constitution?

    1. Collected as a list attached at the very end of the original document
    2. Placed within the original text beside the matters they concerned
    3. Adopted by a second convention called specially for that purpose
    4. Sent to the states one at a time over a period of years
    Show the answer

    Answer: Placed within the original text beside the matters they concerned

    Madison intended his amendments to be woven into the body of the Constitution at the places where each subject arose.

    A separate list at the end was the House's choice, urged by Roger Sherman, not his.

    A second convention is what his opponents pressed for, and Congress sent the twelve amendments together in 1789.

  4. Item 4 of 15

    Delegation is often described as a way for a busy leader to save time, but that description understates what is actually handed over. When a task is delegated, the subordinate gains the authority to make the decisions the task requires, along with the resources the task will consume; a subordinate handed responsibility without authority commensurate with it can only push problems upward, which adds a step rather than removing one. Accountability works differently: the leader who delegated the task is still answerable for its outcome, and therefore keeps a fair interest in how the work is going. The practical difficulty lies in the distance between that interest and meddling. Leaders who manage it well tend to agree in advance on what progress will look like and when it will be reported, rather than asking at odd intervals. There is also a ceiling on how many subordinates one leader can watch with care, a ceiling that armies respect by grouping a handful of elements under each headquarters instead of a dozen. Passing that number rarely causes a visible failure; what it causes instead is a leader who tends to the loudest problem and neglects the rest, a state that is harder to spot and slower to correct.

    In the passage, the word "commensurate" most nearly means

    1. Granted in writing
    2. Shared among peers
    3. Reviewed regularly
    4. Matched in scale
    Show the answer

    Answer: Matched in scale

    A subordinate given responsibility without authority commensurate with it can only push problems upward, so the authority must match the task.

    Written grants and sharing among peers play no part in the sentence.

    Regular reporting belongs to the later advice on tracking progress, not to the authority handed over.

  5. Item 5 of 15

    Before the 1830s, American grain was cut by hand with the cradle, a scythe fitted with wooden fingers that laid the stalks in neat rows, and a skilled worker could harvest about two acres a day. Because ripe wheat has to be cut within a week or two before the grain begins to drop, the size of a farm's crop was limited less by the land it could plant than by the labor it could find at harvest. Cyrus McCormick demonstrated a horse-drawn reaper in Virginia in 1831 but did not patent it until 1834, a year after Obed Hussey patented a rival machine, and their claims to priority were contested for decades. Although a reaper could cut as much grain in a day as several workers with cradles, farmers bought few of them until the mid-1850s. The economic historian Paul David argued in the 1960s that the delay reflected arithmetic rather than conservatism, since a reaper saved enough in wages to repay its price only on farms growing more than a certain acreage of grain. In his account, Midwestern farms grew larger, machines became cheaper and harvest wages rose in the 1850s, pushing many farms past that threshold. Other historians have questioned his assumptions, noting for instance that neighbors could share a single machine, which would have lowered the threshold he calculated.

    What is the main point of the passage?

    1. McCormick's reaper spread slowly because Hussey's patent blocked its sale for years
    2. The reaper's slow adoption has been tied to farm size, an account others dispute
    3. The reaper spread first on small Eastern farms, well before the Midwest adopted it
    4. Farmers ignored the reaper for decades because they distrusted any new machinery
    Show the answer

    Answer: The reaper's slow adoption has been tied to farm size, an account others dispute

    Most of the passage sets out David's view that a reaper paid off only above a certain acreage, then notes that other historians question it.

    Hussey's patent appears only in a dispute over priority, and in David's account the reaper spread as Midwestern farms grew larger.

    David put the delay down to arithmetic rather than conservatism, so distrust of machinery is the view he rejects.

  6. Item 6 of 15

    Most advanced economies now assign monetary policy to central banks that are insulated to some degree from day-to-day political control, an arrangement whose rationale economists developed largely in the late 1970s and the 1980s. The argument begins from a problem of credibility. A government facing an election has a standing temptation to stimulate the economy with easier money, gaining a short burst of output and employment at the cost of higher inflation afterward, and the public, knowing this, expects the higher inflation from the start. The result is inflation without any lasting gain in output, an outcome worse than a firm commitment to stable prices would have produced. Delegating policy to an independent body with a clear mandate is meant to make that commitment believable. In the United States, members of the Federal Reserve Board serve staggered terms of fourteen years, far longer than any presidential term, so that no single administration can easily remake the board. Studies across countries have found that more independent central banks tended to be associated with lower inflation, although critics note that a correlation does not establish a cause, since a society that already values stable prices may be the one that grants independence.

    In the passage, the word "insulated" most nearly means

    1. Shielded
    2. Concealed
    3. Heated
    4. Excluded
    Show the answer

    Answer: Shielded

    Central banks insulated from day-to-day political control are shielded from that pressure, so no single administration can easily remake them.

    Nothing about the banks is hidden, and heat has no place in a sentence about political control.

    Excluded would cut them off entirely, which does not fit insulated to some degree.

  7. Item 7 of 15

    The coalition that expelled Iraqi forces from Kuwait in 1991 joined the armed forces of more than thirty countries, and several Arab members were unwilling to place their troops under an American general. The solution was a parallel command, in which American and most other Western forces answered to General Norman Schwarzkopf while Arab and other Islamic contingents answered to a Saudi commander, Lieutenant General Khalid bin Sultan. The two headquarters worked side by side in Riyadh and linked their staffs through a coordination center that exchanged plans, intelligence and reports around the clock. Military doctrine had long favored unity of command, and some observers expected the arrangement to produce confusion, but it held together through the ground offensive, helped by a clear division of sectors along the front. The air war followed a different principle. A single American officer, Lieutenant General Charles Horner, served as air component commander for the whole coalition, and the sorties of the participating air forces were scheduled in one daily air tasking order issued from his headquarters. The order ran to hundreds of pages, and because the Navy's carriers lacked compatible data links, printed copies had to be flown out to them every day. American doctrine written in the years that followed accepted coordination between two commands as a workable substitute for unity of command whenever a single commander could not be agreed on.

    In the passage, the word "contingents" most nearly means

    1. Events that may or may not happen
    2. Agreements that depend on a condition
    3. Troops contributed by member nations
    4. Reserves kept back for emergencies
    Show the answer

    Answer: Troops contributed by member nations

    Arab and other Islamic contingents answered to a Saudi commander as the Western forces answered to Schwarzkopf: troops each nation contributed.

    Events that may happen and conditional agreements are senses of contingent that do not fit forces placed under a commander.

    Nothing in the passage describes these forces as held back in reserve.

  8. Item 8 of 15

    In a celebrated essay published in 1967, the English historian E. P. Thompson argued that industrialization changed not only what people made but how they experienced time. Before the factory, he suggested, much work was task-oriented: a farmer finished the harvest while the weather held and a weaver might idle early in the week and labor furiously toward its end, so the day was measured by the job rather than by the clock. The mill could not tolerate that rhythm, since expensive machinery earned nothing while it stood still and many hands had to arrive together for any of it to run. Employers therefore enforced the hour with bells, clocks and fines for lateness, and the custom of taking Monday off, which workers had long honored, came under sustained attack. Thompson also saw the lesson reinforced outside the mill, in schools and sermons that praised punctuality as a moral virtue. Subsequent research has qualified his picture, suggesting that working hours were already lengthening and the old holidays shrinking in the eighteenth century, before mechanized factories employed more than a small fraction of the workforce; his central contrast between time that is passed and time that is spent has nonetheless remained influential.

    Why does the author mention schools and sermons?

    1. To show that the demand for punctuality reached beyond the workplace
    2. To suggest that some churches opposed the hours kept in the new mills
    3. To explain how workers learned to operate the machines they tended
    4. To give evidence that task-oriented work survived in the villages for long
    Show the answer

    Answer: To show that the demand for punctuality reached beyond the workplace

    Thompson saw the lesson reinforced outside the mill, in schools and sermons that praised punctuality as a moral virtue.

    The sermons supported the mill's hours rather than opposing them, and no training on machines is mentioned.

    The older task-oriented rhythm is what the mill could not tolerate, not something the schools are cited to show surviving.

  9. Item 9 of 15

    Bombing began as an extension of reconnaissance, with crews dropping small charges by hand on the positions they had been sent to observe. The idea that an air attack might strike the enemy's country rather than its army appeared almost as early. German airships carried that idea to Britain from 1915, crossing the North Sea at night to attack a population that had not been under fire in living memory. The material destruction was modest, but the disruption of industry and the anger of the public were not. Airships proved vulnerable once the defending fighters received incendiary ammunition, and the raids passed to twin-engined bombers, which struck London in daylight in 1917 and exposed how little the existing defenses could do about them. The response was systematic rather than improvised, as squadrons were recalled from France, guns and observer posts were organized into a coordinated network, and a committee examined how the country's air effort was governed. Its conclusion was that an air force divided between the army and the navy could not be directed against objectives that belonged to neither, and in April 1918 Britain merged its two air arms into a single independent service, the first of its kind. The bombing that provoked this reorganization was slight by the standards of the war that followed, yet the institutional argument it produced shaped air power for decades.

    Which statement best expresses the main idea of the passage?

    1. Airship raids destroyed much of British industry and forced a change of government
    2. Bombers replaced airships because their crews could navigate more accurately at night
    3. Attacks on Britain produced a coordinated defense and an independent air service
    4. The army and the navy agreed that bombing should remain a secondary mission
    Show the answer

    Answer: Attacks on Britain produced a coordinated defense and an independent air service

    The passage follows the raids to a coordinated defense network and then to the merger of two air arms into an independent service in 1918.

    The material destruction is called modest, and no change of government is mentioned.

    Airships gave way once fighters had incendiary ammunition, the bombers struck in daylight, and the services were divided rather than agreed.

  10. Item 10 of 15

    For its first three decades the airplane was built mostly of wood, wire and fabric, materials that were light and easy to shape but that absorbed moisture, rotted and burned readily. Aluminum was far lighter than steel, yet in its pure form it was too soft to carry the loads of a structure. That obstacle fell in the first decade of the twentieth century, when the German metallurgist Alfred Wilm found that an aluminum alloy containing small amounts of copper, magnesium and manganese grew markedly harder in the days after it had been heated and quenched, a change now called age hardening. The resulting alloy, sold as duralumin, went first into the frames of rigid airships, whose builders needed strength over great lengths at the lowest possible weight. Hugo Junkers flew an all-metal monoplane in 1915, although that first machine was skinned in steel and proved heavy, and his later designs adopted duralumin covered in corrugated sheet that stiffened the thin skin against buckling. Through the 1930s designers learned to make a smooth metal skin carry a large share of the loads itself instead of merely covering an internal frame, and the stressed-skin airliners of that decade set the pattern that most aircraft have followed since. Wood did not vanish at once, but the direction of development had been settled by a discovery in metallurgy rather than in aerodynamics.

    Which statement best expresses the main idea of the passage?

    1. Junkers showed in 1915 that steel was the best material for covering an airplane
    2. A discovery in metallurgy, not aerodynamics, opened the way to the all-metal airplane
    3. Rigid airships outperformed airplanes once their frames were built of duralumin
    4. Corrugated metal skins stayed the standard for most aircraft through the 1930s
    Show the answer

    Answer: A discovery in metallurgy, not aerodynamics, opened the way to the all-metal airplane

    The passage closes on its point: the direction of development was settled by a discovery in metallurgy rather than in aerodynamics.

    The steel-skinned Junkers of 1915 proved heavy, and airships are never compared with airplanes.

    Corrugated sheet gave way in the 1930s to the smooth stressed skin that most aircraft have followed since.

  11. Item 11 of 15

    The expedition that Ferdinand Magellan led out of Spain in 1519 was not conceived as a voyage around the world. Its purpose was commercial and political: to reach the Spice Islands by sailing west, and so to support the Spanish claim that those islands lay within the half of the globe the Treaty of Tordesillas had assigned to Castile. Five ships and roughly 240 to 270 men, depending on the count, set out, and the expedition found a passage through the southern end of South America only after months of searching along the coast. The Pacific proved far wider than anyone in Europe had supposed, and the crossing, made with dwindling food, cost many lives before land was reached. Magellan himself was killed in 1521 in a battle in the Philippines, and command passed to others who at last reached the Spice Islands. A single ship, the Victoria, under Juan Sebastian Elcano, returned to Spain in 1522 by continuing westward around Africa, with eighteen of the original men aboard. When the survivors reached the Cape Verde Islands, they found that their carefully kept log was a day behind the local calendar, a discrepancy that their westward circuit of the globe itself explained.

    Which of the following can be inferred from the passage?

    1. Most of the men who died were killed in the battle in the Philippines
    2. Elcano commanded the Victoria from the day the fleet left Spain
    3. The expedition lost most of its ships while searching for the passage
    4. Fewer than one in ten of the original men returned to Spain aboard the Victoria
    Show the answer

    Answer: Fewer than one in ten of the original men returned to Spain aboard the Victoria

    Eighteen men returned out of roughly 240 to 270, which is under a tenth of either count.

    The Pacific crossing cost many lives, and the passage never compares that toll with the battle in the Philippines.

    Command passed to others only after Magellan was killed, and the passage does not say when the other ships were lost.

  12. Item 12 of 15

    The Tariff Act of 1930, known by the names of its sponsors, Senator Reed Smoot and Representative Willis Hawley, began as a measure to protect farmers and grew in Congress into a broad increase in duties on thousands of goods. More than a thousand economists signed a petition urging President Herbert Hoover to veto it, warning that it would raise prices at home and provoke other countries to respond in kind. Hoover signed the bill in June 1930, and within a few years many trading partners had raised their own barriers, some in open reprisal. World trade contracted sharply in the early 1930s, and the act has since become a byword for protectionism gone wrong. Many economic historians are more cautious about its role than that reputation suggests, since trade was also shrinking because incomes were collapsing and prices were falling, which by themselves reduce the value of goods crossing borders. Deflation added a further twist, because many duties were fixed sums per unit rather than percentages, so falling prices raised their weight relative to the value of the goods. Whatever its economic effect, the act left a large political legacy, for in 1934 Congress passed the Reciprocal Trade Agreements Act, which let the president negotiate tariff cuts with other countries instead of having Congress set every rate.

    Why does the author mention that many duties were fixed sums per unit?

    1. To show how falling prices made the duties heavier than their rates suggest
    2. To suggest that the petition exaggerated how heavy the new duties would be
    3. To argue that the tariff may have caused most of the fall in world trade
    4. To contrast the 1930 act with the percentage duties set in 1934
    Show the answer

    Answer: To show how falling prices made the duties heavier than their rates suggest

    Because many duties were fixed sums per unit, falling prices raised their weight relative to the value of the goods.

    That makes the duties heavier, so it cannot show the petition overstated them, and the passage doubts the tariff caused most of the fall in trade.

    The 1934 law let the president negotiate tariff cuts; it says nothing about percentage duties.

  13. Item 13 of 15

    Until the middle of the twentieth century, engineers improved telephone lines and radio links largely by trial, since there was no general measure of how much information such a channel could carry. In 1948 Claude Shannon, a mathematician at Bell Laboratories, published a theory that treated information as a quantity, counted in binary digits or bits, and independent of whether a message consisted of speech, text or pictures. His most surprising result concerned noise. Engineers had generally assumed that a noisy channel could be made more reliable only by sending ever more slowly, whereas Shannon showed that every channel has a definite capacity, fixed by its bandwidth and by the strength of the signal relative to the noise, below which messages can in principle be sent with as few errors as one wishes. His proof established that suitable codes existed but gave no recipe for building them, and for decades the codes engineers actually built fell well short of the limit. Only in the 1990s did new families of codes, such as the turbo codes announced in 1993, come close to it. Modern mobile and deep-space links rely on codes of this kind, which add carefully structured redundancy so that a receiver can detect and repair errors without asking for the message to be sent again. The same measure of information also underlies data compression, which strips out the redundancy that such codes deliberately add.

    Why does the author mention what engineers had generally assumed about noisy channels?

    1. To show that Shannon's theory applied only to telephone lines of the time
    2. To set up the contrast that made Shannon's result about noise so surprising
    3. To explain how data compression removes redundancy from a message
    4. To argue that engineers before Shannon had ignored noise altogether
    Show the answer

    Answer: To set up the contrast that made Shannon's result about noise so surprising

    The assumption that a noisy channel could be made reliable only by sending ever more slowly is what made Shannon's result about noise surprising.

    His theory treated information the same whether it was speech, text or pictures, so it was not limited to telephone lines.

    Data compression comes later as another use of the measure, and engineers who slowed down to fight noise had not ignored it.

  14. Item 14 of 15

    Insurers differ not only in what they cover but in who owns them, and the difference shapes whose interests a company is organized to serve. A stock insurer is a corporation owned by shareholders, who supply its capital and receive whatever profit remains once claims and expenses are paid. A mutual insurer has no outside shareholders; its policyholders are its owners, and any surplus it accumulates belongs to them, whether it is returned as dividends, passed on as lower premiums or retained to strengthen the company. One of the oldest American examples is the Philadelphia Contributionship, a mutual fire insurer organized in 1752 with Benjamin Franklin among its founders, which inspected the houses it covered and set its rates according to the hazards it found. Because a mutual has no shares to sell, it must build its capital slowly out of retained surplus, a constraint that can make rapid growth difficult. A stock company can raise money quickly from investors, but it must weigh their demand for returns against the interests of the customers it insures. Both forms have survived side by side in the American market for well over two centuries.

    What does the passage suggest about a mutual insurer compared with a stock insurer?

    1. It can raise capital more quickly because it appeals to outside investors
    2. It hands its entire surplus back to policyholders at the close of each year
    3. It charges lower premiums than a stock insurer for the same coverage
    4. It escapes one balancing act, since its owners and customers are the same people
    Show the answer

    Answer: It escapes one balancing act, since its owners and customers are the same people

    A stock company must weigh its investors' demand for returns against its customers' interests; in a mutual the policyholders are the owners.

    Raising money quickly from investors is the stock company's advantage, since a mutual has no shares to sell.

    A mutual may return, pass on or retain its surplus, and the passage never compares the premiums of the two forms.

  15. Item 15 of 15

    The cities of the Indus Valley, which flourished in what is now Pakistan and northwestern India during the second half of the third millennium BCE, were recognized as a distinct civilization only in the 1920s, and they still resist the kind of explanation that other early civilizations allow. Harappa and Mohenjo-daro were laid out on a broadly regular plan, with main streets running roughly north to south and east to west, covered drains beneath them and many houses provided with their own washing areas. Across a territory larger than that of Egypt or Mesopotamia in the same period, builders used fired bricks whose length, width and thickness kept the same proportions, and traders used stone weights that followed a single standard. Such uniformity implies coordination of some kind, yet excavators have found no building that is clearly a palace and no monument that clearly celebrates a king. The short inscriptions on seals remain undeciphered, so the inhabitants of these cities cannot yet tell us in their own words how their society was governed. After about 1900 BCE the large cities were gradually abandoned, and populations shifted toward smaller settlements farther east. Changes in the monsoon and in the courses of rivers are the leading suspects, although specialists continue to disagree about how much weight each deserves.

    What does the passage suggest about the authority that organized the Indus cities?

    1. It did not display itself the way rulers of other early civilizations did
    2. It was a single king whose palace has since been lost to erosion by the rivers
    3. It lost control of the cities to invaders who arrived from the west
    4. It was replaced by a new line of kings once the cities had been rebuilt
    Show the answer

    Answer: It did not display itself the way rulers of other early civilizations did

    The cities' uniformity implies coordination, yet no building is clearly a palace and no monument clearly celebrates a king, unlike other early civilizations.

    The passage proposes no lost palace, and it names changes in the monsoon and in river courses, not invaders, as the leading suspects.

    The large cities were abandoned for smaller settlements farther east, not rebuilt under new kings.

Situational Judgment

15 situations

  1. Scenario 1 of 15

    Your section's monthly four-hour training block has been cancelled three months running so that the section could meet the production targets your commander set for the quarter. The technical sergeant who runs the training tells you that two of the newer airmen will be overdue on a required qualification next month if the block is cancelled again, and that the others are slipping. The targets stand for the rest of the quarter. Six weeks of it remain.

    1. Restore the full block from this month, and tell the commander at next week's staff meeting what it cost against the quarter's target
    2. Pull the two airmen closest to overdue off production for the hours they need, and keep the block cancelled until the quarter ends
    3. Ask the commander today to release the newer airmen from production for this month's block, and hold the target with the rest
    4. Keep the block cancelled for the six weeks the targets stand, and catch the two qualifications up in the lull that follows the quarter
    5. Propose to the technical sergeant that he train the newer airmen on the job while production runs, and look at the results together after the quarter
    Show the answer

    Most effective: Ask the commander today to release the newer airmen from production for this month's block, and hold the target with the rest

    Least effective: Keep the block cancelled for the six weeks the targets stand, and catch the two qualifications up in the lull that follows the quarter

    Asking the commander today to release the newer airmen meets the requirement this month, at the smallest cost to his target, and asks rather than tells.

    Keeping the block cancelled lets two airmen go overdue on the promise of a lull that three cancelled months have not produced.

    Pulling only the two closest to overdue leaves the rest slipping; restoring the full block cuts the target on the officer's own authority; on-the-job training is a hope checked after the deadline.

  2. Scenario 2 of 15

    You are leaving your office for a meeting with your commander that starts in five minutes. An airman from your flight stops you at the door and asks whether he can talk to you about something personal. He says that it is not an emergency, but he looks shaken. You have not had much contact with him before.

    1. Ask him to put it in an e-mail, so that you can read it properly tonight
    2. Give him the five minutes you have now, and see afterward whether more is needed
    3. Say that you want to hear it properly, and fix a time right after your meeting
    4. Walk him to his supervisor on your way, as the person best placed to hear him first
    5. Tell him that you have to go, and that you will come and find him once you are out
    Show the answer

    Most effective: Say that you want to hear it properly, and fix a time right after your meeting

    Least effective: Ask him to put it in an e-mail, so that you can read it properly tonight

    Saying it deserves a proper hearing and fixing a time right after the meeting takes him seriously and gives him full attention soon.

    Asking for an e-mail turns something personal, from a shaken airman, into a written task and a record he never asked for.

    Promising to find him later gives him no time to count on; five minutes now opens a personal matter only to cut it short; his supervisor is not the one he chose, and may be the subject.

  3. Scenario 3 of 15

    Two months after taking over your section, you notice that paper sign-in sheets are retyped into a spreadsheet every week, which costs about six hours. Your NCO in charge, who runs the process, says it was set up two years ago, before his time, in answer to an audit finding that is on file in the squadron. He has never read the finding, and neither have you.

    1. Ask the NCO to pull the finding and propose a shorter process, since he is the one who runs it
    2. Drop the retyping step now, and keep the paper sheets as the record of who signed in
    3. Read the finding with the NCO this week, and work out together a shorter process that still meets it
    4. Leave the process as it is, and look at it again when the next audit comes around
    5. Have the NCO trim the steps he finds unnecessary, then check what he cut against the finding
    Show the answer

    Most effective: Read the finding with the NCO this week, and work out together a shorter process that still meets it

    Least effective: Drop the retyping step now, and keep the paper sheets as the record of who signed in

    Reading the finding with the NCO this week, then shortening the process together, learns the requirement before anything changes.

    Dropping the retyping step now removes a control born of an audit finding that nobody has read.

    Leaving the NCO to pull the finding means approving a change to a requirement the officer never read; trimming first puts the check after the cut; waiting for the next audit keeps spending six hours a week.

  4. Scenario 4 of 15

    This morning, at your first stand-up as commander of a flight of twenty-two, your flight chief, a master sergeant who has run the flight for three years, introduced you to the flight. He ended by telling them that nothing would change and that the lieutenant would learn how the flight does things, and the flight laughed with him. He is well liked, and the flight's work is good. You had not discussed with him what either of you would say. Your first decision as flight commander, on next month's shift roster, is due to the squadron on Friday.

    1. Let it stand, and settle with him in his office straight after what each of you says to the flight from now on
    2. Add one sentence in the room, that you will learn the flight and that some things will change with you, and leave it at that
    3. Accept it: a chief of his experience has earned it, and the flight will see how you work soon enough
    4. Say nothing about it now, and take it up with him at the end of the week, once the roster decision is made
    5. Leave it until you know the flight better, in a month or so, and raise it with him then
    Show the answer

    Most effective: Let it stand, and settle with him in his office straight after what each of you says to the flight from now on

    Least effective: Accept it: a chief of his experience has earned it, and the flight will see how you work soon enough

    Letting it stand and settling with the chief in his office straight after answers him the same morning, out of the flight's sight, with his standing intact.

    Accepting it lets the chief's words become the flight's view of its new officer, with the officer's consent, and nothing is ever said to him.

    A sentence in the room corrects, in front of the flight, a chief who has run it for three years; the end of the week comes after the roster decision; a month later comes after a month of decisions on his terms.

  5. Scenario 5 of 15

    Your commander has shared with his flight commanders a draft list of names for a six-month deployment that starts in the spring. He asked that it not be discussed until he announces it, which he plans to do on Friday. One of your airmen is on the list. On Tuesday this airman mentions that on Monday he will pay in full for a family trip in the spring, and that the payment cannot be refunded. Draft lists sometimes change before they are announced.

    1. Tell him in confidence that his name is on a draft list, and ask him to keep it to himself
    2. Wait for the announcement on Friday, as it comes before he pays, and go to your commander only if it slips
    3. Tell your commander about the payment today, since only he can have the airman told before Monday
    4. Advise him, without giving a reason, to hold off on any large payment until the end of next week
    5. Tell him and his supervisor about the list now, so that the shop can start planning around his absence
    Show the answer

    Most effective: Tell your commander about the payment today, since only he can have the airman told before Monday

    Least effective: Tell him and his supervisor about the list now, so that the shop can start planning around his absence

    Telling the commander about the payment today brings the one missing fact to the owner of the list, who alone can have the airman told before Monday.

    Telling the airman and his supervisor spreads a draft the commander asked to keep closed, to someone with no need to know yet.

    Waiting for Friday bets the airman's money on the announcement not slipping; advising him to hold off without a reason is a leak in disguise; telling him in confidence breaks the request outright.

  6. Scenario 6 of 15

    Your commander told the group commander at last week's staff meeting that your section's rewiring of the group's training room would be finished by the fifteenth, a date he had from you. Today is the eighth. This morning your flight chief tells you that the control panel the job needs is now due on the nineteenth, and that the section can finish four days after it arrives. Your commander is at a conference out of state until Thursday, reachable by e-mail and by his phone, and the operations officer is acting for him.

    1. Wait for Thursday, and tell him in person, with the new date and what you propose he tells the group
    2. Tell the group's project officer today that the date moves to the twenty-third, and tell the commander on Thursday
    3. Tell the group's project officer today that the date moves to the twenty-third, and let the commander hear it from the group
    4. Take it to the operations officer today, with the new date and your plan, and ask him whether the commander should hear it now or wait for Thursday
    5. E-mail your commander at the conference today with the new finish date and a line he can give the group, copying the operations officer
    Show the answer

    Most effective: E-mail your commander at the conference today with the new finish date and a line he can give the group, copying the operations officer

    Least effective: Tell the group's project officer today that the date moves to the twenty-third, and let the commander hear it from the group

    E-mailing the commander today with the new date and a line for the group tells the man who made the promise of its slip, the same day, with the acting commander copied.

    Telling the group and letting the commander hear it from them takes his promise out of his hands and lets his own group commander surprise him.

    Asking the operations officer leaves the commander to hear it by another's choice; waiting for Thursday sits three days on a slipped date; telling the group first puts it ahead of him on his own promise.

  7. Scenario 7 of 15

    You are a captain. A second lieutenant you supervise, four months into leading a flight, is well liked, and his flight's work is good. His airmen call him by his first name, and on Friday you saw him buying rounds for them at an off-duty gathering. Last week he let several days go by before correcting one of them for repeated lateness.

    1. Raise it at his next feedback session, which falls in two months
    2. Describe to him in private what you saw on Friday, and ask him what he makes of it
    3. Wait until the closeness causes him a real problem with one of his airmen, when the lesson will be clearer to him
    4. Tell him in private that the closeness already costs him, as the late correction showed, and leave him the remedy
    5. Have his flight chief raise it with him, as the person who sees it every day
    Show the answer

    Most effective: Tell him in private that the closeness already costs him, as the late correction showed, and leave him the remedy

    Least effective: Wait until the closeness causes him a real problem with one of his airmen, when the lesson will be clearer to him

    Telling him in private that the closeness already costs him, with the late correction as proof, names the problem early and leaves him the remedy.

    Waiting for a real problem means seeing the damage coming and letting it arrive, on him and on one of his airmen.

    Describing Friday and asking what he makes of it leaves the real link for him to find; sending the flight chief hands a captain's duty to an NCO who works for the lieutenant; the feedback session comes two months late.

  8. Scenario 8 of 15

    You must recommend one of three staff sergeants in your flight for a sought-after position on the squadron staff. One of the three has played on the squadron's off-duty softball team with you for two years, and the flight knows that you get along well. On the record he is, in your view, slightly the strongest of the three. Your commander makes the final choice and usually follows the flight commander's recommendation. Your recommendation is due next week.

    1. Make the pick on merit, and mention the softball team to your commander when you send the recommendation
    2. Recommend the stronger of the other two, so that nobody can call the choice a favor to a friend
    3. Make the pick on merit, and put your reasons in writing in case the choice is ever questioned
    4. Settle on your pick, then ask your flight chief whether he sees the three the same way
    5. Send your commander all three names without an order, and let him choose among them
    Show the answer

    Most effective: Make the pick on merit, and mention the softball team to your commander when you send the recommendation

    Least effective: Recommend the stronger of the other two, so that nobody can call the choice a favor to a friend

    Picking on merit and mentioning the softball team recommends the strongest sergeant and gives the commander the one fact that could make it look like a favor.

    Recommending one of the other two takes the position from the strongest sergeant to protect the officer's image.

    The flight chief's view is a real check, but from a subordinate after the pick, and the commander still knows nothing; written reasons prepare a defense and tell nobody; three unranked names avoid the job.

  9. Scenario 9 of 15

    A month ago you asked your section for ideas to cut wasted time. Twelve came in, several of them from airmen who had never put an idea forward before. With your NCOs you have chosen the two that the section has time to pursue this quarter. Of the other ten, some are sound but costly, and some would not work. The section meets on Friday.

    1. Announce the two ideas on Friday, and explain to the section how the choice was made
    2. Start work on the two ideas this week, and let the results show the section which ones were chosen
    3. Post all twelve ideas on Friday, with a line against each one giving the decision and the reason for it
    4. Announce the two ideas on Friday, and thank everyone else warmly for having taken part
    5. See that each of the ten hears in person, before Friday, why the idea is not going ahead
    Show the answer

    Most effective: Post all twelve ideas on Friday, with a line against each one giving the decision and the reason for it

    Least effective: Start work on the two ideas this week, and let the results show the section which ones were chosen

    Posting all twelve ideas with a decision and a reason for each answers every proposer and shows the section that all twelve were read.

    Starting work and letting the results show leaves ten people who answered the call hearing nothing at all.

    Telling each of the ten in person is warmer, but the section never sees the whole picture; explaining the method answers no one about his or her own idea; thanks offer courtesy in place of a reason.

  10. Scenario 10 of 15

    You lead a six-person team that is setting up an equipment demonstration for a visiting general at eight o'clock tomorrow morning. At five in the afternoon a key component fails. Your technicians doubt that it can be repaired on site, and a replacement cannot arrive before noon tomorrow. Without it, about half of the demonstration still works. Your commander, who asked for the full demonstration, is on a flight and lands at ten tonight.

    1. Send the team home to rest, and settle the way ahead with the commander in the morning
    2. Put the team on a reduced demonstration now, and call the commander when he lands with that plan
    3. Keep the team on the failed component through the night, and report once it works or the visit begins
    4. Start the team on what still works, and leave the facts in a message for the commander to read on landing
    5. Hold the team until the commander lands, and do tonight whatever he then decides
    Show the answer

    Most effective: Put the team on a reduced demonstration now, and call the commander when he lands with that plan

    Least effective: Keep the team on the failed component through the night, and report once it works or the visit begins

    Starting the reduced demonstration now and calling the commander with that plan when he lands uses the evening and still lets him change it.

    Working the failed component all night stakes the visit on a repair the technicians doubt, and the commander may learn of it in front of the general.

    A message with the facts brings him a problem without a plan; holding the team until he lands wastes five hours; sending it home loses the evening and tells him at the last moment.

  11. Scenario 11 of 15

    Your flight of twenty has a group chat on their phones, which the flight uses for shift swaps and rides; you are not in it. A new squadron commander arrived two weeks ago and has not yet met your flight; he visits the shop on Friday. This morning your flight chief, a master sergeant, showed you on his phone a run of jokes about the new commander's first all-call that a senior airman has been posting there for a week, with a dozen replies from the flight. The chief was laughing, said the airman is the flight's comedian, and asked you not to make a thing of it.

    1. Drop it: the chief knows his flight, and a commander who cannot take a joke from the ranks will hear worse than this
    2. Say at tomorrow's stand-up, to the whole flight, that the chat is no place for jokes about the commander, without naming anyone
    3. Have the flight chief bring the senior airman to your office this afternoon, and tell the two of them together that it stops today
    4. Tell the flight chief that it stops today and that stopping it is his, and say why it matters with a new commander
    5. Let it go for now, and have the chief show you the chat again next week before you decide anything
    Show the answer

    Most effective: Tell the flight chief that it stops today and that stopping it is his, and say why it matters with a new commander

    Least effective: Drop it: the chief knows his flight, and a commander who cannot take a joke from the ranks will hear worse than this

    Telling the flight chief that it stops today, that stopping it is his, and why it matters with a new commander uses the chain and corrects his tolerance too.

    Dropping it ratifies what the chief tolerated, and a flight that has not met its commander goes on mocking him with its officer's consent.

    Calling both to the office takes over a correction the chief can make himself; a general word at the stand-up comes a day later and leaves the chief out; waiting a week lets the chief decide what is seen next.

  12. Scenario 12 of 15

    The wing has asked your squadron for one airman for six months at the wing command post, where he will deal with the wing staff every day. Your commander wants a name from each flight commander by Friday, and he will choose among them. Your flight chief proposes the senior airman the flight can most easily spare, whose work is adequate and whose record is thin. The flight's strongest senior airman is the one your busiest section leans on.

    1. Propose the strongest senior airman, and tell the commander the cost to his section and how you will cover it
    2. Send the flight chief's name up with nothing on the airman's record, which the commander did not ask for
    3. Go back to the flight chief with the tasking, and settle with him the name the wing will see
    4. Propose the flight chief's airman, and give the commander his record plainly beside the name
    5. Put the flight chief's airman forward as a solid worker, which he is as far as his own job goes
    Show the answer

    Most effective: Propose the strongest senior airman, and tell the commander the cost to his section and how you will cover it

    Least effective: Put the flight chief's airman forward as a solid worker, which he is as far as his own job goes

    Proposing the strongest senior airman, with the cost to his section and the plan to cover it, sends the right airman and gives the commander an informed choice.

    Calling the flight chief's airman a solid worker dresses a thin record as a solid one, and the commander chooses on a false picture.

    Stating that airman's record plainly is honest, but still puts up the one easiest to spare; going back to the flight chief sends down a call the officer has the facts for; the name alone gives nothing to weigh.

  13. Scenario 13 of 15

    At this morning's shift-change brief, which was running long, a staff sergeant on the day shift started to raise a concern about the way the night shift had left a lift, and you cut him off and moved on to the next item. An hour later your flight chief, a master sergeant, tells you that the sergeant took it badly in front of his crew, and that the concern was a real one: the lift had been left with a load on it, which the section's practice forbids. The flight chief has had the load taken off and will speak to the night shift lead tonight. The sergeant is on the floor until four.

    1. Rely on the flight chief to smooth it over with the sergeant, and take up the concern with him at next week's safety meeting
    2. Go with the flight chief to him on the floor this afternoon, say you cut him short, and hear the concern with the chief there
    3. Go back to it at tomorrow's brief, say in front of the shift that you cut him short and that he was right, and hear him out then
    4. Thank the flight chief for taking care of the lift, and say a word to the sergeant about it when you next see him
    5. Find him on the floor before noon, tell him you cut him short at the brief, and take the concern from him there
    Show the answer

    Most effective: Find him on the floor before noon, tell him you cut him short at the brief, and take the concern from him there

    Least effective: Rely on the flight chief to smooth it over with the sergeant, and take up the concern with him at next week's safety meeting

    Finding him on the floor before noon, owning the interruption and taking the concern there puts it right in person, the same day.

    Leaving the repair to the chief and the concern to next week teaches the shift that raising a safety concern at the brief gets a sergeant cut off and nothing more.

    Going with the chief comes later and makes it two on one; tomorrow's brief comes a day late; a word at the next chance puts off what his crew saw happen today.

  14. Scenario 14 of 15

    Your flight is being inspected this week by a team from the group. One of the inspectors is a captain you went through training with. Over lunch he tells you that he found the tool records in one of your shops two months out of date, and that he means to leave it out of his report, as the shop has already started bringing them up to date. It would be the only finding against your flight. The team briefs your commander on Friday.

    1. Let him write the report as he chooses, and tell your commander today what was found and what you are doing about it
    2. Ask him to keep the finding in his report, since it is true, and to note the fix the shop has begun
    3. Show him what the shop has done since he looked, and ask him whether that changes the finding
    4. Accept his offer with thanks, and bring the records up to date before anyone acts on the report
    5. Accept his offer, and tell your commander about the records once the shop has brought them up to date
    Show the answer

    Most effective: Ask him to keep the finding in his report, since it is true, and to note the fix the shop has begun

    Least effective: Accept his offer with thanks, and bring the records up to date before anyone acts on the report

    Asking him to keep the finding and note the fix keeps the record true, credits the shop, and lets the commander hear exactly what was found.

    Accepting the offer and quietly fixing the records lets an official report say that nothing was wrong.

    Telling the commander directly comes close, but a report known to be incomplete still goes to him; showing the fix works the inspector toward a softer finding; telling the commander after the fix comes after the report has said otherwise.

  15. Scenario 15 of 15

    A newly commissioned lieutenant has been attached to your flight for a month to learn the work before he takes over a flight of his own. Twice this week he has corrected your flight chief, a master sergeant, in front of airmen; both times the flight chief was in fact wrong on the point, and the lieutenant was right. The flight chief has come to you about the manner, not the substance. Three weeks of the month remain.

    1. Tell the lieutenant that he was right on both points and wrong in the manner, and have him settle it with the flight chief himself
    2. Tell the flight chief that the lieutenant was right on both points, and that you will speak to him about the manner
    3. Tell the lieutenant to correct the flight chief only in private from now on, and leave it there
    4. Tell the lieutenant to leave corrections of the flight chief to you from now on, and say nothing to the flight chief
    5. Ask the flight chief to let it go, as the lieutenant will be gone in three weeks
    Show the answer

    Most effective: Tell the lieutenant that he was right on both points and wrong in the manner, and have him settle it with the flight chief himself

    Least effective: Ask the flight chief to let it go, as the lieutenant will be gone in three weeks

    Telling the lieutenant he was right on both points and wrong in the manner, then having him settle it, names both halves and makes the repair his.

    Asking the flight chief to let it go waves his complaint away on the calendar, and the lieutenant hears nothing.

    Answering the flight chief alone takes the repair out of the lieutenant's hands; a private-only rule comes without its reason; leaving corrections to the officer silences a judgment that was right twice.

Physical Science

15 questions

  1. Item 1 of 15

    What is an element, in chemical terms?

    1. Any mixture of two or more substances
    2. A compound made from two identical atoms bonded together
    3. A pure substance made of a single type of atom
    4. A liquid formed by dissolving a solid in water
    5. A charged particle formed from a single atom
    Show the answer

    Answer: A pure substance made of a single type of atom

    An element is a pure substance made of one type of atom, every atom carrying the same number of protons.

    A mixture combines substances without bonding them, a solid dissolved in water forms a solution, and a charged atom is an ion.

    A compound joins different elements, so two identical atoms bonded together, as in oxygen gas, form a molecule of an element.

  2. Item 2 of 15

    Venus is the hottest planet in the solar system mainly because of what?

    1. Being the closest planet to the Sun
    2. Constant volcanic eruptions on its surface
    3. A surface made mostly of reflective ice and snow
    4. A thick carbon dioxide atmosphere trapping heat
    5. Rapid friction from its fast rotation
    Show the answer

    Answer: A thick carbon dioxide atmosphere trapping heat

    Venus's thick carbon dioxide atmosphere traps heat in a strong greenhouse effect.

    Mercury is closer to the Sun yet cooler, so distance alone cannot explain it.

    Venus has no ice cover and rotates very slowly, and volcanoes are not what keeps its whole surface hot.

  3. Item 3 of 15

    A resistor carries 2 amps of current and has a resistance of 5 ohms. What is the voltage across it?

    1. 20 volts
    2. 25 volts
    3. 10 volts
    4. 14 volts
    5. 50 volts
    Show the answer

    Answer: 10 volts

    Ohm's law: voltage = current × resistance, so 2 × 5 = 10 volts.

    20 doubles the current before multiplying, 25 squares the resistance, and 50 multiplies the current by the resistance twice.

    14 doubles the sum of the two values, and no form of Ohm's law adds current to resistance.

  4. Item 4 of 15

    Heat transfer through electromagnetic waves, such as heat reaching Earth from the Sun, is called what?

    1. Conduction
    2. Radiation
    3. Convection
    4. Absorption
    5. Reflection
    Show the answer

    Answer: Radiation

    Radiation carries heat as electromagnetic waves and needs no matter, which is how the Sun's heat crosses empty space.

    Conduction needs contact between particles and convection needs a moving fluid, so neither crosses a vacuum.

    Absorption is energy taken up by a material and reflection is energy bouncing off it; neither is a way heat travels.

  5. Item 5 of 15

    Which of these best describes a mixture?

    1. A single pure element
    2. A type of chemical bond between two atoms
    3. A combination of substances not chemically bonded
    4. A new and noticeably different substance formed as the direct result of a chemical reaction
    5. A substance that always has a fixed, uniform composition
    Show the answer

    Answer: A combination of substances not chemically bonded

    A mixture combines substances that are not chemically bonded and keep their own properties, like salt stirred into water.

    A pure element and a chemical bond are not combinations of substances, and the product of a reaction is a new substance.

    A fixed, uniform composition marks a pure substance; a mixture's proportions can vary.

  6. Item 6 of 15

    In a double replacement reaction, what typically happens?

    1. A single element decomposes into two separate elements
    2. One element bonds with oxygen to form an oxide
    3. Two compounds trade ions to form two new ones
    4. A compound absorbs energy without forming a new substance
    5. One of the two starting compounds must already be a gas
    Show the answer

    Answer: Two compounds trade ions to form two new ones

    In a double replacement reaction, two compounds swap ions: AB + CD gives AD + CB.

    A single element cannot break down into other elements, and an element combining with oxygen to form an oxide is a synthesis reaction.

    Absorbing energy with no new substance is a physical change, and no starting compound needs to be a gas; these reactions often run in solution.

  7. Item 7 of 15

    Which of these is generally true about solubility as water temperature increases?

    1. Most solids dissolve more as water warms
    2. Solids dissolve in smaller amounts as water gets warmer
    3. Temperature has no effect on solubility
    4. Gases dissolve better in warm water
    5. All solids become completely insoluble once water reaches its boiling point
    Show the answer

    Answer: Most solids dissolve more as water warms

    Most solids dissolve more in warmer water, which is why more sugar dissolves in hot tea than in iced tea.

    Less solid dissolving as water warms is the exception, not the rule, and temperature clearly matters.

    Gases are the case that runs the other way, dissolving less in warm water, and boiling makes no solid insoluble.

  8. Item 8 of 15

    According to the law of conservation of energy, when a ball rolls down a hill, what generally happens to its total mechanical energy, ignoring friction?

    1. It steadily increases as the ball speeds up
    2. It disappears once the ball reaches the bottom
    3. It converts entirely into potential energy as the ball reaches the bottom
    4. It stays constant, converting between potential and kinetic forms
    5. It converts entirely into thermal energy by the bottom
    Show the answer

    Answer: It stays constant, converting between potential and kinetic forms

    Without friction, mechanical energy is conserved: potential energy turns into kinetic energy as the ball rolls down, and their sum stays constant.

    The ball speeds up because energy changes form, not because the total grows, and the energy does not disappear.

    At the bottom potential energy is at its lowest and kinetic energy at its highest, and with no friction nothing turns it into heat.

  9. Item 9 of 15

    An electromagnet produces a magnetic field by

    1. Current passing through a coil of wire
    2. Heating a magnet until it melts
    3. Rubbing two insulators together repeatedly
    4. Spinning a coil of wire rapidly with no current flowing
    5. Freezing a conductor to near absolute zero
    Show the answer

    Answer: Current passing through a coil of wire

    An electric current through a coil of wire produces a magnetic field, made stronger by an iron core.

    Heating a magnet weakens or destroys its magnetism, and rubbing insulators builds static charge, not a magnetic field.

    With no current the coil makes no field, and cooling a conductor makes no field by itself.

  10. Item 10 of 15

    What is inertia?

    1. The tendency of an object to gradually speed up over time
    2. The force that pulls objects toward Earth
    3. The energy an object has because it is moving
    4. The tendency to resist a change in motion
    5. The total distance an object has traveled
    Show the answer

    Answer: The tendency to resist a change in motion

    Inertia is an object's tendency to resist any change in its motion, at rest or moving; more mass means more inertia.

    Inertia keeps an object from speeding up on its own, and the pull toward Earth is gravity, a force.

    Energy of motion is kinetic energy, and total distance traveled describes a path, not a property of the object.

  11. Item 11 of 15

    How does the transit method help astronomers detect exoplanets?

    1. By observing a periodic dip in starlight as a planet crosses it
    2. By directly photographing the surface features and terrain of the planet
    3. By measuring artificial radio signals said to be sent from the planet
    4. By directly detecting the faint visible light the planet gives off at night
    5. By measuring a small, periodic wobble in the star's position in the sky
    Show the answer

    Answer: By observing a periodic dip in starlight as a planet crosses it

    When a planet crosses in front of its star, it blocks a little of the star's light, and the dip repeats every orbit.

    Tracking a wobble in the star's position is a separate method, and radio signals from a planet play no part.

    The transit method never sees the planet itself: neither its surface nor its own faint light.

  12. Item 12 of 15

    Two objects are dropped from the same height in a vacuum, with no air resistance, one twice as heavy as the other. Which reaches the ground first?

    1. The heavier object, because more gravitational force acts on it
    2. The lighter object, because it has less mass to accelerate
    3. The lighter object falls slower at first, then catches up
    4. Whichever object has more surface area, since drag still slows the other one down
    5. Both, because gravity accelerates all objects at the same rate regardless of mass
    Show the answer

    Answer: Both, because gravity accelerates all objects at the same rate regardless of mass

    Without air resistance, gravity gives every object the same acceleration, about 9.8 meters per second squared, so both land together.

    The heavier object does feel twice the force, but it has twice the mass to accelerate, so the two effects cancel.

    The lighter object neither lags at first nor wins, and with no air, surface area causes no drag.

  13. Item 13 of 15

    Why do ionic compounds such as table salt typically have much higher melting points than most covalent compounds?

    1. Ionic compounds have no true chemical bonds holding them together
    2. Covalent compounds are generally built from heavier atoms than ionic ones
    3. Ionic compounds conduct electricity, and that is what raises the melting point
    4. The rigid ionic lattice needs far more energy to break apart
    5. Ionic bonds are actually the weaker of the two bond types
    Show the answer

    Answer: The rigid ionic lattice needs far more energy to break apart

    In an ionic solid, each ion is held by strong electrical attraction to its neighbors throughout a rigid lattice, which takes much energy to break.

    Most covalent compounds melt once the weak forces between their molecules give way, without breaking their bonds.

    Ionic bonds are real and strong, atomic mass does not explain the gap, and solid salt does not even conduct electricity.

  14. Item 14 of 15

    About how fast does sound travel through air at room temperature?

    1. About 3.43 meters per second
    2. About 34 meters per second
    3. About 343 meters per second
    4. About 3,430 meters per second
    5. About 34,300 meters per second
    Show the answer

    Answer: About 343 meters per second

    Sound travels through air at room temperature at about 343 meters per second, roughly 767 miles per hour.

    3.43 meters per second is a jogging pace and 34 meters per second about highway driving speed, both far too slow.

    3,430 and 34,300 meters per second are ten and a hundred times the real figure.

  15. Item 15 of 15

    What are metalloids, such as silicon and boron?

    1. Elements that behave chemically in much the same familiar way as ordinary metals typically do
    2. Elements with properties intermediate between metals and nonmetals
    3. Elements found within the noble gas group
    4. Compounds formed by combining two different pure metals
    5. Elements that conduct electricity as well as copper does
    Show the answer

    Answer: Elements with properties intermediate between metals and nonmetals

    Metalloids such as silicon and boron sit along the staircase line of the periodic table, with properties between those of metals and nonmetals.

    They do not behave like ordinary metals, and they conduct electricity far less well than copper; silicon is a semiconductor.

    The noble gases are a separate group, and a metalloid is an element, not a compound of two metals.

Table Reading

15 questions

The real test is taken at a workstation. On a narrow screen the table scrolls under its headings.

X\Y -17-16-15-14-13-12-11-10-9-8-7-6-5-4-3-2-10+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17
+17 107109110112114115116117117119121123125126127129131132134135136138139141143145146147149150151153154155156
+16 107109111113115116118119119119121123125127128130132134135137137139141142144146147149149151152154155157158
+15 109111112114116116118120121121122124126128130131133135137139139140142143145147148150151152154156157158159
+14 111112112114116118118120122123124125127129131133134135137139140142142144146148149151152153155156158160161
+13 111113114114116118118120122123125126128130132133134136138139141143144145147149150152153154156158160162163
+12 112114116116118120120122123125127128129131133135136137139140142144146147149150152154155156157159161163165
+11 113115117118119120122123124126128129129131133135137139141141143145147149151152153155156157158160162164165
+10 114116118120121121123125125127129131131132134136138140142143145146148150152153155156157159160160162164166
+9 114116118120122123125126127129130132133134136138140141143144146147148150152154156158158160162162162164166
+8 114116118120122124126127129130132134135136138139141142144145147148149151153155157159160161163163164166167
+7 116117118120122124126128130131133135136138140141143144146147148149151153155157158160161162164165165167168
+6 118118120121123125127129131133135136138140140142143145147149150151152154156157158160162164166167167168169
+5 119119121122124126128129131133135137139141142143145146147149150152153155157158160162164166167168169170171
+4 120121123124124126128130132134136138139141143145146147148150152154155157158160162164165167168169169170172
+3 121121123125125127129131133135137139140142144146148149150151152154156158159161163164166168169171171172173
+2 123123124126127128130132134136138140142143145147149150151151153155157159161162164165167169171172173174174
+1 125125126128128129131133135137139141143144146148150151153153154156158160162164165166168170171173174175176
0 127127128130130131133134136138140142144145147149151152154155156158159161163165166167169171172174176176178
-1 129129130131132133135136137139141143145145147149151153155156158158160162164166167167169171173174176178180
-2 131131132133134135136136138140142144146147149150152154156157158159161162164166168169170172174176178179180
-3 132133134135136137138138138140142144146148150151153155156158159160162164166166168170171173175177178180182
-4 133134136137138139140140140142144146148148150152154156157159161162163165167168169171172174176178178180182
-5 135136138139140141142142142142144146148150152153155157159161162163163165167169171172174175177179180182184
-6 137137139141142143144144144144145147149151153155155157159161163165165166168170172174175177179180182183185
-7 138138140142142144146146146146147148150152154156156158160161163165166168170172173175177178180181183185187
-8 140140140142142144146147148148149150151153155156158160161163165167167168170172174175177179181183185185187
-9 142142142143144145147148150150151152153155156158159160161163165167168170172173175176178179181183185187188
-10 144144144145146147148150152152153154154156158159161161161163165167168170172174176178179180181183185187189
-11 146146146147148149150150152153155156156158160161163163163164166167169171173175177179180182183183185187189
-12 147148148149150151152152153154156158158159161162163165165166167169169171173175177179180182184185186188189
-13 148149150151152153154154155156158159160161162163164166167168169170171173175176178180181183185187188190191
-14 149151152153154155156156157158160161161162164165166168169170171172173174176178180181183184186188189191193
-15 151152153154155157158158159160161161162164166167168169169171172173175176178180181183184185187189189191193
-16 152154154156157157159160161162163163164166167169169170171173174175177177179181182184185185187189190192194
-17 154155156158158159161162163164165165166168169169171172173174176176178179181183184186187187188190192194195
  1. Item 1 of 15

    X = -14, Y = +15

    1. 116
    2. 112
    3. 113
    4. 109
    5. 114
    Show the answer

    Answer: 114

  2. Item 2 of 15

    X = -11, Y = +15

    1. 118
    2. 117
    3. 121
    4. 120
    5. 116
    Show the answer

    Answer: 118

  3. Item 3 of 15

    X = -16, Y = +7

    1. 117
    2. 114
    3. 116
    4. 119
    5. 120
    Show the answer

    Answer: 117

  4. Item 4 of 15

    X = -9, Y = +13

    1. 122
    2. 125
    3. 123
    4. 124
    5. 128
    Show the answer

    Answer: 122

  5. Item 5 of 15

    X = -4, Y = +8

    1. 140
    2. 136
    3. 132
    4. 135
    5. 131
    Show the answer

    Answer: 136

  6. Item 6 of 15

    X = -7, Y = +4

    1. 135
    2. 133
    3. 142
    4. 134
    5. 136
    Show the answer

    Answer: 136

  7. Item 7 of 15

    X = -16, Y = -9

    1. 147
    2. 142
    3. 144
    4. 140
    5. 138
    Show the answer

    Answer: 142

  8. Item 8 of 15

    X = +5, Y = +9

    1. 146
    2. 149
    3. 148
    4. 151
    5. 147
    Show the answer

    Answer: 148

  9. Item 9 of 15

    X = +6, Y = +9

    1. 151
    2. 157
    3. 150
    4. 149
    5. 153
    Show the answer

    Answer: 150

  10. Item 10 of 15

    X = -1, Y = -1

    1. 153
    2. 151
    3. 146
    4. 150
    5. 149
    Show the answer

    Answer: 151

  11. Item 11 of 15

    X = +12, Y = +6

    1. 168
    2. 166
    3. 164
    4. 167
    5. 161
    Show the answer

    Answer: 164

  12. Item 12 of 15

    X = +7, Y = -5

    1. 168
    2. 172
    3. 167
    4. 164
    5. 170
    Show the answer

    Answer: 167

  13. Item 13 of 15

    X = +12, Y = -3

    1. 172
    2. 170
    3. 173
    4. 171
    5. 176
    Show the answer

    Answer: 173

  14. Item 14 of 15

    X = +8, Y = -10

    1. 171
    2. 172
    3. 176
    4. 178
    5. 174
    Show the answer

    Answer: 174

  15. Item 15 of 15

    X = +12, Y = -17

    1. 183
    2. 190
    3. 187
    4. 188
    5. 185
    Show the answer

    Answer: 187

Instrument Comprehension

15 questions

  1. Item 1 of 15

    Which airplane matches the two dials?

    Item 1: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 4 of 4

    Horizon: diving, banked 60° to the right.

    Compass: heading northeast, away from the viewer, to the right.

    The other three bank left; two of them also head east or north.

  2. Item 2 of 15

    Which airplane matches the two dials?

    Item 2: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 1 of 4

    Horizon: climbing, banked 30° to the left.

    Compass: heading north, away from the viewer.

    The others head east, fly level heading northwest, or bank right.

  3. Item 3 of 15

    Which airplane matches the two dials?

    Item 3: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 3 of 4

    Horizon: level flight, banked 15° to the right.

    Compass: heading southeast, toward the viewer and to the right.

    The others bank 45°, head northwest, or bank left.

  4. Item 4 of 15

    Which airplane matches the two dials?

    Item 4: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 1 of 4

    Horizon: diving, banked 30° to the left.

    Compass: heading southwest, toward the viewer and to the left.

    The others head south, fly level heading south, or bank right.

  5. Item 5 of 15

    Which airplane matches the two dials?

    Item 5: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 2 of 4

    Horizon: wings level, climbing.

    Compass: heading south, toward the viewer.

    The others fly level, head north, or head southwest.

  6. Item 6 of 15

    Which airplane matches the two dials?

    Item 6: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 1 of 4

    Horizon: diving, banked 15° to the right.

    Compass: heading northwest, away from the viewer, to the left.

    The others bank 45°, bank left, or head southeast.

  7. Item 7 of 15

    Which airplane matches the two dials?

    Item 7: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 2 of 4

    Horizon: diving, banked 60° to the right.

    Compass: heading north, away from the viewer.

    The others bank left, fly level heading northwest, or head west.

  8. Item 8 of 15

    Which airplane matches the two dials?

    Item 8: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 3 of 4

    Horizon: level flight, banked 45° to the left.

    Compass: heading southeast, toward the viewer and to the right.

    The others bank 90°, climb, or head northwest.

  9. Item 9 of 15

    Which airplane matches the two dials?

    Item 9: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 2 of 4

    Horizon: wings level, steep dive.

    Compass: heading west, nose to the left.

    The others head east, northwest, or north.

  10. Item 10 of 15

    Which airplane matches the two dials?

    Item 10: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 1 of 4

    Horizon: diving, banked 30° to the left.

    Compass: heading west, nose to the left.

    The others bank right, bank 60°, or head northwest.

  11. Item 11 of 15

    Which airplane matches the two dials?

    Item 11: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 3 of 4

    Horizon: steep dive, banked 45° to the left.

    Compass: heading northwest, away from the viewer, to the left.

    The others bank right, head west in a gentler dive, or head southeast.

  12. Item 12 of 15

    Which airplane matches the two dials?

    Item 12: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 2 of 4

    Horizon: diving, banked 90° to the left.

    Compass: heading northwest, away from the viewer, to the left.

    The others bank 60°, head southeast, or head west in a steep dive.

  13. Item 13 of 15

    Which airplane matches the two dials?

    Item 13: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 2 of 4

    Horizon: level flight, banked 90° to the right.

    Compass: heading northwest, away from the viewer, to the left.

    The others head southeast, head west, or climb.

  14. Item 14 of 15

    Which airplane matches the two dials?

    Item 14: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 1 of 4

    Horizon: steep climb, banked 90° to the left.

    Compass: heading southwest, toward the viewer and to the left.

    The others head northeast, head west banked right, or head southeast.

  15. Item 15 of 15

    Which airplane matches the two dials?

    Item 15: the artificial horizon and the compass
    1. Airplane 1 of 4
    2. Airplane 2 of 4
    3. Airplane 3 of 4
    4. Airplane 4 of 4
    Show the answer

    Answer: Airplane 4 of 4

    Horizon: climbing, banked 90° to the right.

    Compass: heading east, nose to the right.

    The others bank left, head north, or climb steeply.

Block Counting

15 questions

Figure 1 of 3

A pile of blocks, five of them numbered 1 to 5.
  1. How many other blocks does block 1 touch?

    Show the answer

    Answer: 4

    One below, one beside (block 2), two above: four.

    Its contact with block 4, above, is out of sight; missing it gives 3.

    5 to 7 count blocks that sit close without sharing a face.

    Block 1 and the 4 blocks it touches, shown in color.
  2. How many other blocks does block 2 touch?

    Show the answer

    Answer: 6

    Three beside (block 1 among them), three above: six.

    Only its end shows, and two contacts above, block 4's included, are out of sight; missing one gives 5.

    7 to 9 count blocks that only look adjacent.

    Block 2 and the 6 blocks it touches, shown in color.
  3. How many other blocks does block 3 touch?

    Show the answer

    Answer: 3

    One below, two beside (block 5 and the upright block): three.

    All three contacts are in view; 2 misses one of them.

    4 to 6 count blocks that only look adjacent.

    Block 3 and the 3 blocks it touches, shown in color.
  4. How many other blocks does block 4 touch?

    Show the answer

    Answer: 5

    Three below (blocks 1 and 2 among them), one above, one beside: five.

    Only its end shows, and its contacts with blocks 1 and 2 are out of sight; missing them gives 4 or 3.

    6 and 7 count blocks that only look adjacent.

    Block 4 and the 5 blocks it touches, shown in color.
  5. How many other blocks does block 5 touch?

    Show the answer

    Answer: 3

    One below, two beside (block 3 among them): three.

    All three contacts are in view.

    4 to 7 count blocks that sit close without sharing a face.

    Block 5 and the 3 blocks it touches, shown in color.

Figure 2 of 3

A pile of blocks, five of them numbered 1 to 5.
  1. How many other blocks does block 1 touch?

    Show the answer

    Answer: 3

    One below (block 2), one beside, one above: three.

    All three contacts are in view; 2 misses one of them.

    4 to 6 count blocks that only look adjacent.

    Block 1 and the 3 blocks it touches, shown in color.
  2. How many other blocks does block 2 touch?

    Show the answer

    Answer: 5

    Three below (block 5 among them), block 1 above, block 3 beside: five.

    All five contacts are in view; 2 to 4 leave some of them out.

    6 counts a block that only looks adjacent.

    Block 2 and the 5 blocks it touches, shown in color.
  3. How many other blocks does block 3 touch?

    Show the answer

    Answer: 5

    Three below (block 5 among them), one above, block 2 beside: five.

    Only its end shows, and two contacts below, block 5's included, are out of sight; missing one gives 4.

    6 to 8 count blocks that only look adjacent.

    Block 3 and the 5 blocks it touches, shown in color.
  4. How many other blocks does block 4 touch?

    Show the answer

    Answer: 4

    One beside, three above (block 5 among them): four.

    Only its end shows, and two contacts above, block 5's included, are out of sight; missing one gives 3.

    5 to 7 count blocks that only look adjacent.

    Block 4 and the 4 blocks it touches, shown in color.
  5. How many other blocks does block 5 touch?

    Show the answer

    Answer: 7

    Two below (block 4 among them), three beside, blocks 2 and 3 above: seven.

    Only its end shows, and its contacts with blocks 3 and 4 are out of sight; missing them gives 6 or 5.

    4 also misses a visible block; 8 counts one that only looks adjacent.

    Block 5 and the 7 blocks it touches, shown in color.

Figure 3 of 3

A pile of blocks, five of them numbered 1 to 5.
  1. How many other blocks does block 1 touch?

    Show the answer

    Answer: 4

    One beside, three above (blocks 3 and 4 among them): four.

    Only its end shows, and its contacts with blocks 3 and 4 are out of sight.

    5 to 8 count blocks that only look adjacent.

    Block 1 and the 4 blocks it touches, shown in color.
  2. How many other blocks does block 2 touch?

    Show the answer

    Answer: 5

    Three below (block 4 among them), block 5 beside, one above: five.

    Two contacts below, block 4's included, are out of sight; missing one gives 4.

    6 to 8 count blocks that only look adjacent.

    Block 2 and the 5 blocks it touches, shown in color.
  3. How many other blocks does block 3 touch?

    Show the answer

    Answer: 6

    Three below (block 1 among them), two beside (block 4 among them), one above: six.

    Only its end shows, and two contacts below, block 1's included, are out of sight; missing them gives 5 or 4.

    2 and 3 also miss blocks that are in view.

    Block 3 and the 6 blocks it touches, shown in color.
  4. How many other blocks does block 4 touch?

    Show the answer

    Answer: 9

    Three below, two beside, four above: nine, blocks 1, 2, 3 and 5 among them.

    Only its end shows, and five contacts are out of sight: two below, three above.

    Missing some of the five gives 5 to 8.

    Block 4 and the 9 blocks it touches, shown in color.
  5. How many other blocks does block 5 touch?

    Show the answer

    Answer: 6

    Three below (block 4 among them), two beside (block 2 among them), one above: six.

    Two contacts below, block 4's included, are out of sight; missing them gives 5 or 4.

    7 and 8 count blocks that only look adjacent.

    Block 5 and the 6 blocks it touches, shown in color.

Aviation Information

15 questions

  1. Item 1 of 15

    The term stalling speed can be misleading because a wing can stall whenever

    1. the landing gear fails to retract during the climb
    2. the engine's carburetor ices up during the descent
    3. its airspeed drops below the manufacturer's published value
    4. its critical angle of attack is exceeded, regardless of airspeed
    5. its flaps are retracted below the maneuvering speed
    Show the answer

    Answer: its critical angle of attack is exceeded, regardless of airspeed

    A wing stalls whenever it exceeds its critical angle of attack, at any airspeed, attitude or power setting.

    The published stalling speed holds only for one weight, configuration and load factor, so a wing can stall above it.

    Landing gear, carburetor ice and flap position are not what makes a wing stall.

  2. Item 2 of 15

    If a pilot must continually hold back pressure on the control column to maintain a given attitude, this indicates a need to

    1. reduce the engine's manifold pressure
    2. trim the airplane nose-down
    3. retract the landing gear
    4. trim the airplane nose-up
    5. extend the flaps further
    Show the answer

    Answer: trim the airplane nose-up

    Constant back pressure means the airplane wants to pitch nose-down, so the pilot trims nose-up until the pressure is relieved.

    Trimming nose-down would demand even more back pressure.

    The trim, not power, gear or flaps, is the control meant to relieve a steady control pressure.

  3. Item 3 of 15

    Under standard sea-level conditions, the average atmospheric pressure of 29.92 inches of mercury is equal to approximately

    1. 760 millibars
    2. 2,000 millibars
    3. 1,500 millibars
    4. 1,013 millibars
    5. 500 millibars
    Show the answer

    Answer: 1,013 millibars

    Standard sea-level pressure is 29.92 inches of mercury, or 1,013.2 millibars.

    760 is the same pressure in millimeters of mercury, not millibars.

    500 millibars is reached near 18,000 feet, and 1,500 or 2,000 millibars exceed any sea-level pressure.

  4. Item 4 of 15

    Ground effect is a condition of improved performance normally encountered up to an altitude equal to about

    1. one wingspan above the surface
    2. the airplane's pattern altitude
    3. the length of the takeoff roll
    4. one wing chord above the surface
    5. the height of the traffic pattern downwind leg
    Show the answer

    Answer: one wingspan above the surface

    Ground effect is felt within about one wingspan of the surface, where the ground reduces wingtip vortices and induced drag.

    A wing chord is a far smaller distance, and pattern altitude and the downwind leg are far higher.

    The takeoff roll is a length along the runway, not a height.

  5. Item 5 of 15

    In an airplane's weight and balance, the abbreviation CG stands for

    1. center of gravity
    2. ground clearance
    3. center of pressure
    4. glide path
    5. center of lift
    Show the answer

    Answer: center of gravity

    CG stands for center of gravity, the point through which the airplane's whole weight acts and around which it would balance.

    Center of pressure and center of lift name the point where the lift force acts, not the weight.

    Ground clearance and glide path do not abbreviate to CG.

  6. Item 6 of 15

    On an airplane with a constant-speed propeller, engine power output is indicated by the

    1. tachometer
    2. manifold pressure gauge
    3. airspeed indicator
    4. altimeter
    5. oil pressure gauge
    Show the answer

    Answer: manifold pressure gauge

    With a constant-speed propeller, the governor holds rpm steady, so the manifold pressure gauge shows power output.

    The tachometer indicates power only on a fixed-pitch propeller, where rpm varies with the throttle.

    Airspeed, altitude and oil pressure gauges do not measure engine power.

  7. Item 7 of 15

    In a typical intentional spin, the first turn results in an altitude loss of approximately

    1. 100 feet, with roughly half that for each following turn
    2. 1,000 feet, with roughly double that for each following turn
    3. 1,000 feet, with roughly half that for each following turn
    4. 500 feet, with the same loss for every following turn
    5. 2,000 feet, with roughly half that for each following turn
    Show the answer

    Answer: 1,000 feet, with roughly half that for each following turn

    A typical light airplane loses about 1,000 feet in the first spin turn and roughly half that in each turn after.

    100 and 2,000 feet are the wrong starting figures.

    The turns after the first cost less altitude, not double and not the same as the first.

  8. Item 8 of 15

    Class B airspace, which surrounds the nation's busiest airports and can resemble an upside-down wedding cake in profile, requires aircraft to

    1. remain below 10,000 feet AGL at all times
    2. obtain an ATC clearance before entering
    3. carry a Mode C transponder but need no clearance
    4. avoid all published instrument procedures
    5. operate only under visual flight rules
    Show the answer

    Answer: obtain an ATC clearance before entering

    Every aircraft needs an ATC clearance before entering Class B airspace, and ATC then separates the traffic inside it.

    A Mode C transponder is required too, but it never replaces the clearance.

    Class B contains the airport's instrument procedures and IFR traffic, and no rule keeps aircraft inside it below 10,000 feet AGL.

  9. Item 9 of 15

    The gyroscopic principle by which a spinning gyro remains fixed in the plane in which it is spinning, regardless of how its mounting is tilted, is called

    1. precession
    2. rigidity in space
    3. rigidity of the gimbal rings
    4. gyroscopic drift
    5. deflective force
    Show the answer

    Answer: rigidity in space

    Rigidity in space keeps a spinning gyro's plane of rotation fixed however its mounting is tilted; attitude and heading indicators rely on it.

    Precession is the gyro tilting or turning in response to a deflective force, not its resistance to tilt.

    The rigidity belongs to the spinning rotor, not the gimbal rings, and drift is a slow error of the gyro, not this property.

  10. Item 10 of 15

    Rain falling from a thunderstorm at the surface indicates that hail aloft

    1. never falls more than one-half inch in diameter
    2. can only occur below the freezing level
    3. has completely stopped forming
    4. is definitely absent from the storm
    5. may still be present above the melting level
    Show the answer

    Answer: may still be present above the melting level

    Hail falling through air above freezing melts and can reach the ground as rain, so hail may still be present aloft.

    Rain at the surface therefore proves neither that hail is absent nor that it has stopped forming.

    Hail forms above the freezing level, not below it, and hailstones can be much larger than half an inch.

  11. Item 11 of 15

    For a limited time, which airspace measure protects persons and property from an existing or imminent hazard and keeps sightseeing aircraft from congesting above an event?

    1. Military training route
    2. Temporary flight restriction
    3. National security area
    4. Terminal radar service area
    5. Local airport advisory
    Show the answer

    Answer: Temporary flight restriction

    A temporary flight restriction is issued for a limited time to protect people and property from a hazard and keep sightseeing aircraft from crowding over an event.

    A military training route is a route for military flights, and a national security area surrounds sensitive ground facilities.

    A terminal radar service area offers radar service to VFR traffic, and a local airport advisory is a service on the field, not a restriction.

  12. Item 12 of 15

    Fog that forms when cold, dry air moves over warm water and that resembles rising smoke is called

    1. ice fog
    2. radiation fog
    3. steam fog
    4. advection fog
    5. upslope fog
    Show the answer

    Answer: steam fog

    Steam fog, or sea smoke, forms when cold, dry air moves over warmer water and the rising moisture condenses like smoke.

    Advection fog is warm, moist air over a colder surface, and radiation fog forms over land on calm, clear nights.

    Upslope fog forms as moist air rises up sloping terrain, and ice fog needs temperatures far below freezing.

  13. Item 13 of 15

    The barometric pressure setting window on an altimeter's face, used to adjust the instrument for nonstandard pressure, is sometimes called the

    1. Kollsman window
    2. pressure chamber
    3. calibrated leak
    4. aneroid chamber
    5. static chamber
    Show the answer

    Answer: Kollsman window

    The Kollsman window shows the barometric setting; set to the local altimeter setting, the altimeter reads the correct altitude.

    An aneroid chamber is a sealed capsule inside the instrument that senses pressure, not a window on its face.

    The calibrated leak belongs to the vertical speed indicator, and pressure chamber and static chamber name no window either.

  14. Item 14 of 15

    A red, illuminated stop bar lies across a taxiway a pilot must cross, but ATC has just cleared the aircraft to proceed onto the runway. The pilot should

    1. wait for the taxiway centerline lights to turn green instead
    2. treat it the same as a clearance bar light
    3. cross immediately since the clearance was already given
    4. never cross it and query ATC for clarification
    5. cross only if visibility is above 1,200 feet RVR
    Show the answer

    Answer: never cross it and query ATC for clarification

    A pilot never crosses an illuminated red stop bar, even with an ATC clearance, and asks ATC to resolve the conflict.

    The green lead-on lights come on only once the stop bar goes dark, so waiting for them alone leaves the conflicting clearance unresolved.

    A clearance bar is a row of yellow lights at a holding position, and no visibility value makes crossing a lit stop bar acceptable.

  15. Item 15 of 15

    A high-wing airplane whose wing struts attach approximately halfway out on the wing and carry flight and landing loads to the fuselage has a

    1. biplane wing
    2. semi-cantilever wing
    3. weight-shift wing
    4. full cantilever wing
    5. tricycle wing
    Show the answer

    Answer: semi-cantilever wing

    Struts attached about halfway out that carry the wing's loads to the fuselage make it a semi-cantilever wing.

    A full cantilever wing carries its loads through internal structure alone, without external struts.

    A biplane has two wings stacked, a weight-shift aircraft is steered by moving the pilot's weight, and tricycle names a landing gear.

Explore each subtest

Format, scoring, and five more free questions on every subtest page.

The three TBAS simulators

Airplane Tracking in play: a green reticle locked on a red aircraft over a dark blue field, with the lower lane tracked at the bottom.

Airplane Tracking (ATT / AHTT)

Simulator · 2 min

Keep the gunsight on one airplane with the joystick and the box on the other with the pedals.

It measures your ability to track a moving target in two dimensions, horizontal and vertical.

How the subtest works
Multitasking in play: four panels at once, a word check, an addition to key in, a gauge to hold in the green and four numbered tiles.

Multitasking (MTT)

Simulator · 5 min

Juggle a letter memory drill, arithmetic, a drifting gauge and radio calls, all four at once.

It measures time sharing: keeping several tasks going at once, not arithmetic or memory as such.

How the subtest works
Directional Orientation in play: the aircraft view of a compound and its four parking lots, next to the tracker map with the heading.

Directional Orientation (DOT / UAV)

48 questions

Use the drone's heading on the map to click the parking lot a voice names in the aircraft view.

It measures spatial orientation: you determine the aircraft's position relative to a target.

How the subtest works

And the twelve AFOQT subtests

Train on every subtest.
Know your rank.

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