What this section covers: Arithmetic word problems.
10 free practice questions
Click an answer: you see at once whether it is right, with the explanation.
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Question 1A student scores 82, 90, 75 and 88 on four quizzes. What is her average score?
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Answer: A — 83.75.
Add the scores (82 + 90 + 75 + 88 = 335) and divide by the number of quizzes: 335 ÷ 4 = 83.75. 335 is the total, not the average.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 2How much simple interest does $2,500 earn in 3 years at 4% per year?
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Answer: B — $300.
Simple interest = principal × rate × time = 2,500 × 0.04 × 3 = $300. $100 is one year's interest; $2,800 is the balance, not the interest.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 3The ratio of boys to girls in a class of 40 students is 3 to 5. How many boys are in the class?
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Answer: D — 15.
The ratio has 3 + 5 = 8 parts, so each part is 40 ÷ 8 = 5 students. Boys = 3 × 5 = 15. 25 is the number of girls.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 4A bus leaves at 2:15 p.m. and travels 234 miles at an average speed of 52 miles per hour. At what time does it arrive?
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Answer: C — 6:45 p.m..
Time = distance ÷ rate = 234 ÷ 52 = 4.5 hours, which is 4 hours 30 minutes. 2:15 p.m. plus 4 hours 30 minutes is 6:45 p.m.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 5A ribbon 3.5 feet long is cut into pieces that are each 6 inches long. How many pieces are there?
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Answer: B — 7.
3.5 feet = 3.5 × 12 = 42 inches, and 42 ÷ 6 = 7 pieces. 21 comes from multiplying 3.5 by 6 instead of converting to inches first.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 6The price of a bicycle rises from $80 to $92. By what percent did the price increase?
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Answer: A — 15%.
The increase is $12. Percent increase = increase ÷ original price = 12 ÷ 80 = 0.15 = 15%. Dividing by the new price (12 ÷ 92) gives about 13%, which is wrong.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 7Ana can paint a fence in 8 hours. Ben can paint the same fence in 12 hours. How long will it take them working together?
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Answer: C — 4.8 hours.
Ana paints 1/8 and Ben 1/12 of the fence per hour; together 3/24 + 2/24 = 5/24 per hour. Time = 24/5 = 4.8 hours. 10 hours is the average of the two times, which is too slow.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 8Sam's average on his first four tests is 85. What score does he need on the fifth test to raise his average to 87?
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Answer: D — 95.
He needs a total of 5 × 87 = 435 points. He has 4 × 85 = 340, so he needs 435 - 340 = 95 on the fifth test.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 9On a map, 1 inch represents 25 miles. Two towns are 3.4 inches apart on the map. What is the real distance between them?
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Answer: B — 85 miles.
Multiply the map distance by the scale: 3.4 × 25 = 85 miles.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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Question 10Lena buys 3 notebooks at $2.35 each and 2 pens at $1.20 each. She pays with a $20 bill. How much change should she get?
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Answer: A — $10.55.
Notebooks cost 3 × 2.35 = $7.05 and pens 2 × 1.20 = $2.40, for a total of $9.45. Change = $20.00 - $9.45 = $10.55. $9.45 is the cost, not the change.
Checked against: Official ASVAB — Arithmetic Reasoning (AR): ability to solve arithmetic word problems
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