ASVAB Arithmetic Reasoning Practice Test
Word problems by hand, every step shown. Here are 10 ASVAB arithmetic reasoning questions, each with the answer and the reason.
Updated by the Tigertest team. Covers eight of the CAT-ASVAB subtests in test order with the real time limits. Assembling Objects uses figures and is not included. Minimum AFQT scores vary by branch and change with recruiting needs.
- 1.
A recruit runs 3 miles in 24 minutes. At the same pace, how many minutes will it take to run 5 miles?
- A.
40 minutes
- B.
36 minutes
- C.
42 minutes
- D.
45 minutes
Answer: A.The pace is 24 ÷ 3 = 8 minutes per mile, so 5 miles takes 5 × 8 = 40 minutes. Adding 12 minutes for each extra mile beyond 3 gives the same result.
- A.
- 2.
A car travels 300 miles on 12 gallons of gasoline. How many miles per gallon does the car get?
- A.
20 miles per gallon
- B.
24 miles per gallon
- C.
30 miles per gallon
- D.
25 miles per gallon
Answer: D.Miles per gallon is miles divided by gallons: 300 ÷ 12 = 25. Estimating with 10 gallons gives 30, which is why 30 is a tempting but wrong answer.
- A.
- 3.
A train departs at 9:45 a.m. and arrives at 2:15 p.m. the same day. How long is the trip?
- A.
4 hours 15 minutes
- B.
4 hours 30 minutes
- C.
5 hours 30 minutes
- D.
4 hours 45 minutes
Answer: B.From 9:45 to 12:45 is 3 hours, and from 12:45 to 2:15 is 1 hour 30 minutes, for a total of 4 hours 30 minutes. Subtracting the clock numbers directly (2:15 minus 9:45) does not work across noon.
- A.
- 4.
The price of a jacket rose from $60 to $75. What was the percent increase?
- A.
15%
- B.
20%
- C.
25%
- D.
30%
Answer: C.The increase is $15. Percent increase is change divided by the original price: 15 ÷ 60 = 0.25, or 25 percent. Dividing by the new price of $75 gives 20 percent, which is wrong.
- A.
- 5.
A pump removes water from a 900-gallon pool at 15 gallons per minute. How long will it take to empty the pool?
- A.
45 minutes
- B.
50 minutes
- C.
60 minutes
- D.
75 minutes
Answer: C.Time equals volume divided by rate: 900 ÷ 15 = 60 minutes. Check: 15 × 60 = 900.
- A.
- 6.
Sam buys 3 notebooks at $2.25 each and 2 pens at $1.10 each. If he pays with a $10 bill, how much change does he receive?
- A.
$0.95
- B.
$1.15
- C.
$2.05
- D.
$1.05
Answer: D.Notebooks cost 3 × $2.25 = $6.75 and pens cost 2 × $1.10 = $2.20, for a total of $8.95. Change is $10.00 - $8.95 = $1.05.
- A.
- 7.
A rope 36 feet long is cut into pieces that are each 2.25 feet long. How many pieces are there?
- A.
12 pieces
- B.
14 pieces
- C.
16 pieces
- D.
18 pieces
Answer: C.Divide the total length by the piece length: 36 ÷ 2.25 = 16. Check: 16 × 2 = 32 and 16 × 0.25 = 4, so 16 × 2.25 = 36.
- A.
- 8.
One painter can paint a room in 6 hours. Another painter can paint the same room in 3 hours. Working together, how long will they take to paint the room?
- A.
2 hours
- B.
3 hours
- C.
4 hours
- D.
4.5 hours
Answer: A.In one hour the painters finish 1/6 + 1/3 = 1/6 + 2/6 = 1/2 of the room, so together they take 2 hours. Averaging the two times (4.5 hours) is a common error; working together is always faster than the faster worker alone.
- A.
- 9.
The temperature at noon was 14 degrees Fahrenheit. By midnight it was -9 degrees. By how many degrees did the temperature drop?
- A.
5 degrees
- B.
14 degrees
- C.
23 degrees
- D.
25 degrees
Answer: C.The drop is 14 - (-9) = 14 + 9 = 23 degrees. Subtracting 9 from 14 (getting 5) ignores that the final temperature is below zero.
- A.
- 10.
Two cars start 300 miles apart and drive toward each other, one at 55 mph and the other at 65 mph. In how many hours will they meet?
- A.
2 hours
- B.
2.5 hours
- C.
3 hours
- D.
3.5 hours
Answer: B.Together they close the gap at 55 + 65 = 120 miles per hour, so they meet after 300 ÷ 120 = 2.5 hours.
- A.
Drill every arithmetic reasoning question in the ASVAB Arithmetic Reasoning drill: questions you miss come back until you have mastered them. Then take a timed practice test with the Arithmetic Reasoning section in it.
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