ASVAB Study GuideArithmetic Reasoning Practice Test 1
Tap an answer to check it instantly and read the explanation. 10 questions: 4 easy, 4 medium and 2 hard.
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Question 1 easy
If Mike can finish his assignment in half an hour, what part can he finish in 15 minutes?
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Correct answer: B — $$\frac{1}{2}$$
Half an hour is equal to 30 minutes. The fraction of the assignment finished in 15 minutes is $$\frac{15}{30} = \frac{1}{2}$$
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Question 2 hard
Alan and Bob are $$\frac{1}{2}$$ mile apart and run toward each other at constant speeds. Alan runs at 5.5 miles per hour, and Bob runs at 6.5 miles per hour. How long will it take for them to meet?
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Correct answer: A — 2 minutes 30 seconds
Their combined speed is $$5.5 + 6.5 = 12$$ miles per hour. The time to meet is 0.5 miles / 12 mph $$= \frac{1}{24}$$ hours. Converting to minutes: $$(\frac{1}{24}) \times 60 = 2.5$$ minutes, which is exactly 2 minutes 30 seconds.
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Question 3 medium
Tim has $4.40 in his piggy bank in dimes and quarters. If he has three times as many dimes as quarters and no other coins, how many quarters does he have?
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Correct answer: C — 8
Let x be the number of quarters. Then the number of dimes is $$3x$$. The total value equation: $$0.25x + 0.10(3x) = 4.40 \Rightarrow 0.55x = 4.40 \Rightarrow x = 8$$ quarters.
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Question 4 easy
The numbers 14, 22, 18, and x have an average equal to 16. What is x?
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Correct answer: A — 10
The sum of the four numbers is $$16 \times 4 = 64$$. Therefore, $$x = 64 - (14 + 22 + 18) = 64 - 54 = 10$$
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Question 5 easy
If 30 of 150 laborers work overtime, about what percentage of the laborers work overtime?
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Correct answer: A — 20%
The percentage of laborers working overtime is $$(\frac{30}{150}) \times 100\% = 20\%$$
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Question 6 medium
Sophia and Alfonzo have a total of 24 books. If Alfonzo has twice the number of books Sophia has, how many books does Sophia have?
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Correct answer: C — 8
Let x be the number of books Sophia has. Alfonzo has $$2x$$ books. Their sum is $$x + 2x = 24 \Rightarrow 3x = 24 \Rightarrow x = 8$$
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Question 7 hard
A troop walked to a camp and then returned. The return trip was 1.5 miles shorter than the trip to the camp. If the total distance walked was 8.5 miles, how many miles was the trip to the camp?
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Correct answer: A — 5
Let x be the distance to the camp. The return distance is $$x - 1.5$$. Total distance: $$x + (x - 1.5) = 8.5 \Rightarrow 2x = 10 \Rightarrow x = 5$$ miles.
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Question 8 medium
Find the second number in a sequence of four consecutive odd numbers that add up to 64.
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Correct answer: B — 15
Let the consecutive odd numbers be n, $$n+2$$, $$n+4$$, and $$n+6$$. Their sum is $$4n + 12 = 64 \Rightarrow 4n = 52 \Rightarrow n = 13$$. The sequence is 13, 15, 17, 19. The second number is 15.
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Question 9 medium
Noah doubled the number of magazine subscriptions he sold each week for four weeks. If he sold 48 subscriptions during the fourth week, how many did he sell the first week?
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Correct answer: C — 6
He sold 48 in week 4. Week 3: $$\frac{48}{2} = 24$$. Week 2: $$\frac{24}{2} = 12$$. Week 1: $$\frac{12}{2} = 6$$
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Question 10 easy
When Bob received his shipment of 40,000 tomatoes, 15% were too badly bruised to sell. How many could he still sell?
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Correct answer: A — 34,000
The percentage of sellable tomatoes is $$100\% - 15\% = 85\%$$. Number of sellable tomatoes is $$40{,}000 \times 0.85 = 34{,}000$$