AFOQT · Academic Aptitude and Quantitative composites
Arithmetic Reasoning
Arithmetic Reasoning is the AFOQT subtest in which you solve word problems with arithmetic and pick the answer among five.
- Items
- 25
- Time
- 29 minutes
- Answer options
- 5
- Composites
- Academic Aptitude, Quantitative
- Calculator
- Not allowed
- Guessing penalty
- None
Screens of the trainer
The subtest
Measures
The subtest measures how well you read a short everyday situation, choose the operations it calls for and carry the arithmetic through. Its score counts toward the Academic Aptitude and Quantitative composites.
It does not count toward the Pilot, CSO or ABM composites.
Format
The 25 items run in 29 minutes, just over a minute per item.
No calculator is allowed.
Scoring
The score is the number of correct answers, and there is no penalty for guessing.
The composites it feeds are reported as percentiles from 1 to 99.
Item types
Word problems
The problems deal with distance, speed and travel time, the volume of a container, money and prices, and what percent one amount is of another.
Some problems mix units, such as a trip timed in hours with a question about minutes, or miles turned into inches on a map.
Free practice test
Item 1 of 5
A backyard swimming pool holds 900 cubic feet of water when it is full. After a week of hot weather, the pool is four fifths full. How many cubic feet of water are in the pool?
Show the answer
Answer: 720
Four fifths of the pool's 900 cubic feet is 900 ÷ 5 × 4 = 720.
Item 2 of 5
A cyclist rides 36 miles in 135 minutes, keeping one pace throughout. At that pace, how many miles does the cyclist cover in the next 45 minutes?
Show the answer
Answer: 12
The cyclist needs 135 ÷ 36 = 3.75 minutes for each mile, so in the next 45 minutes the cyclist covers 45 ÷ 3.75 = 12.
Item 3 of 5
Only 40% of the seats in a small hall were filled when the curtain went up. An usher walking the rows at that moment counted 168 empty seats. How many seats are in the hall altogether?
Show the answer
Answer: 280
If only 40% of the seats were filled, the 168 empty ones are the other 60% of the hall. The hall therefore holds 168 ÷ 0.60 = 280.
Item 4 of 5
A shopper buys 4 folders at $2.30 each and 6 pens that all cost the same. The total comes to $18.50. What does one pen cost?
Show the answer
Answer: $1.55
The four folders cost 4 × $2.30 = $9.20, so the six pens account for $18.50 − $9.20 = $9.30. One pen therefore costs $9.30 ÷ 6 = $1.55.
Item 5 of 5
A field kitchen draws 3 gallons of water a minute for the first 25 minutes of a meal service, then the faucet is opened wider and the kitchen draws 5 gallons a minute for the next 40 minutes. A 60-gallon reserve is also used at the end. Using 4 quarts in a gallon, how many quarts does the service use in all?
Show the answer
Answer: 1,340
The first 25 minutes draw 3 × 25 = 75 gallons and the next 40 minutes draw 5 × 40 = 200 gallons, and the reserve adds 60 more: 75 + 200 + 60 = 335 gallons. At 4 quarts to the gallon that comes to 335 × 4 = 1,340 quarts.
The Frontline Forge trainer
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Instant feedback
Training mode shows the correct answer after each item, with the calculation that reaches it.
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The real format
Test mode runs 25 items with five options in 29 minutes, the count and time of the real subtest, and you can move back to an earlier item. The five items above come from the trainer's bank of 400 word problems, which also covers ratios, work rate, mixtures and averages.
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Ranked against other test-takers
Each score is ranked against the scores of other test-takers. The Statistics page plots the ranking of every attempt, so you see whether you are beating more test-takers than before.