ASVAB Arithmetic Reasoning Practice Test 2
- Word Problems 2
- 15 questions
- 18 minutes
These 15 word problems cover the kinds of everyday math that appear on the ASVAB Arithmetic Reasoning subtest. Before you calculate, decide exactly what the question asks for; many wrong options are the right answer to a slightly different question.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A recipe that makes 4 servings uses 112 cups of rice. How many cups of rice are needed to make 10 servings?
Correct answer: C
One serving needs 1.5 ÷ 4 = 0.375 cup, so 10 servings need 0.375 × 10 = 3.75 cups, which is 334 cups. You can also scale directly: 10 servings is 2.5 times the recipe, and 1.5 × 2.5 = 3.75.
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Question 2
A truck travels 378 miles on 18 gallons of fuel. How many miles per gallon does the truck get?
Correct answer: A
Miles per gallon = miles ÷ gallons = 378 ÷ 18 = 21. Check: 21 × 18 = 378.
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Question 3
The price of a pair of boots drops from $40 to $34. By what percent did the price decrease?
Correct answer: B
The price fell by $6, and a percent decrease is measured from the original price: 6 ÷ 40 = 0.15 = 15%. Dividing by the new price (6 ÷ 34) gives about 17.6%, and 85% is the share of the original price that remains.
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Question 4
Six workers can build a stone wall in 8 days. At the same rate, how many days would it take 4 workers to build the same wall?
Correct answer: D
The job takes 6 × 8 = 48 worker-days. With 4 workers, it takes 48 ÷ 4 = 12 days. Fewer workers need more time, so 513 (which uses 8 × 4 ÷ 6) cannot be right.
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Question 5
A rectangular lot measures 120 feet by 80 feet. A fence will be built all the way around it, with a post at every corner and every 10 feet along the sides. How many posts are needed?
Correct answer: B
The perimeter is 2 × (120 + 80) = 400 feet, which makes 400 ÷ 10 = 40 gaps. On a closed loop the number of posts equals the number of gaps, so 40 posts. The answer 44 counts each corner post twice (13 + 9 posts per pair of sides, doubled).
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Question 6
A guard shift starts at 2245 (military time) and lasts 9 hours 30 minutes. At what time does the shift end?
Correct answer: A
From 2245, 9 hours later is 0745 the next morning, and 30 more minutes makes 0815. Another way: 22:45 + 9:30 = 32:15, and subtracting 24 hours for the new day gives 0815.
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Question 7
The sum of three consecutive whole numbers is 78. What is the largest of the three numbers?
Correct answer: C
Three consecutive numbers average to the middle one: 78 ÷ 3 = 26, so the numbers are 25, 26 and 27. The largest is 27; 26 is the middle number.
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Question 8
A mother is now 3 times as old as her son. In 12 years, she will be twice as old as he will be then. How old is the son now?
Correct answer: B
Let the son's age be s, so the mother is 3s. In 12 years: 3s + 12 = 2(s + 12), which gives 3s + 12 = 2s + 24 and s = 12. Check: the mother is 36 now and will be 48 when the son is 24. The answer 36 is the mother's age.
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Question 9
A salesperson earns $500 a week plus a 6% commission on everything she sells. Last week she sold $8,500 worth of goods. How much did she earn last week?
Correct answer: C
The commission is 0.06 × $8,500 = $510, and adding the base pay gives $500 + $510 = $1,010. The answer $510 is the commission alone, and $551 uses 0.6% instead of 6%.
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Question 10
A store mixes 20 pounds of peanuts that cost $4 per pound with 10 pounds of cashews that cost $7 per pound. What is the cost per pound of the mixture?
Correct answer: A
The total cost is 20 × $4 + 10 × $7 = $80 + $70 = $150 for 30 pounds, so the mixture costs $150 ÷ 30 = $5.00 per pound. The answer $5.50 is the simple average of $4 and $7, which ignores that there are twice as many pounds of peanuts.
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Question 11
On a map, 1 inch represents 25 miles. Two towns are 412 inches apart on the map. How far apart are the towns in real life?
Correct answer: D
Multiply the map distance by the scale: 4.5 × 25 = 112.5 miles. The answer 100 ignores the half inch, and 5.6 comes from dividing 25 by 4.5.
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Question 12
A training run is 2 miles long. One mile equals 5,280 feet. How many feet long is the run?
Correct answer: D
Two miles is 2 × 5,280 = 10,560 feet. The answer 2,640 is half a mile, which comes from dividing instead of multiplying.
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Question 13
A drawer holds 8 black socks and 4 white socks. One sock is taken out without looking. What is the probability that it is white?
Correct answer: B
There are 4 white socks out of 12 in all, so the probability is 412 = 13. The answer 12 compares white socks with black socks (4 to 8) instead of with the total.
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Question 14
A car leaves a base at 1:00 p.m. and drives at 40 miles per hour. A second car leaves the same base at 2:00 p.m. on the same road, driving at 60 miles per hour. At what time will the second car catch up with the first?
Correct answer: C
At 2:00 p.m. the first car is 40 miles ahead. The second car gains 60 − 40 = 20 miles each hour, so it needs 40 ÷ 20 = 2 hours and catches up at 4:00 p.m. Both cars have then gone 120 miles.
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Question 15
A room has four walls, each 12 feet long and 8 feet high, with no windows. One gallon of paint covers 400 square feet. Paint is sold only in whole gallons. How many gallons are needed to give the walls two coats?
Correct answer: A
The walls cover 4 × 12 × 8 = 384 square feet, so two coats need 768 square feet of coverage. 768 ÷ 400 = 1.92, which rounds up to 2 whole gallons.
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