ASVAB Arithmetic Reasoning Practice Test
- Word Problems
- 12 questions
- 15 minutes
Arithmetic Reasoning is the ASVAB's word-problem subtest, covering rates, percents, ratios, work, money and distance. Calculators are not allowed on the ASVAB, so practice by hand, and check what the question asks for before you calculate: many wrong choices answer a 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.
Your result
- 0 correct
- 0 wrong
- 0 blank
-
Question 1
A convoy travels at 45 miles per hour for 3 hours and then at 60 miles per hour for 2 hours. How many miles does the convoy travel in all?
Correct answer: B
Find each part separately: 45 × 3 = 135 miles and 60 × 2 = 120 miles, for a total of 255 miles. The answer 262.5 comes from averaging the two speeds, which does not work when the times are different.
-
Question 2
A recruit answered 42 out of 56 questions correctly on a practice test. What percent of the questions did the recruit answer correctly?
Correct answer: D
Percent correct = 42 ÷ 56 = 0.75, or 75%. The value 25% is the percent of questions the recruit missed (14 ÷ 56).
-
Question 3
On a ship, the ratio of sailors to officers is 9 to 2. There are 220 people on board, and each is either a sailor or an officer. How many officers are on the ship?
Correct answer: B
The ratio has 9 + 2 = 11 parts, so each part is 220 ÷ 11 = 20 people, and the officers make up 2 × 20 = 40. The answer 20 is the size of only one part, and 180 is the number of sailors.
-
Question 4
One pump can fill a water tank in 6 hours. A second pump can fill the same tank in 3 hours. If both pumps work together, how long will it take to fill the tank?
Correct answer: A
Together the pumps fill 1/6 + 1/3 = 1/2 of the tank per hour, so the whole tank takes 2 hours. The answer 4.5 hours is the average of the two times, but working together must be faster than either pump alone.
-
Question 5
A soldier earns $2,400 per month and saves 15% of each paycheck. How much does the soldier save in one year?
Correct answer: C
The monthly savings are 0.15 × $2,400 = $360, and 12 months × $360 = $4,320. The answer $360 is the savings for only one month, and $28,800 is the full year's pay.
-
Question 6
Three pounds of coffee cost $21.75. At the same price per pound, how much do 5 pounds cost?
Correct answer: A
One pound costs $21.75 ÷ 3 = $7.25, so 5 pounds cost 5 × $7.25 = $36.25. The answer $108.75 multiplies the price of 3 pounds by 5, as if it were the price of one pound.
-
Question 7
Jordan deposits $1,500 in an account that pays 4% simple interest per year. How much interest will the account earn in 3 years?
Correct answer: C
Simple interest = principal × rate × time = $1,500 × 0.04 × 3 = $180. The answer $1,680 is the total balance after 3 years, not the interest earned.
-
Question 8
A tent that normally costs $250 is marked down 20%. At the register, an extra 10% is taken off the sale price. What is the final price?
Correct answer: B
After the first discount the price is $250 × 0.80 = $200, and the extra 10% off gives $200 × 0.90 = $180. Adding the discounts to get 30% off ($175) is wrong because the second discount applies to the lower sale price.
-
Question 9
Two trucks leave the same base at the same time and drive in opposite directions. One travels at 50 miles per hour and the other at 40 miles per hour. After how many hours will they be 225 miles apart?
Correct answer: A
Moving in opposite directions, the distance between the trucks grows by 50 + 40 = 90 miles each hour, so 225 ÷ 90 = 2.5 hours. The answer 22.5 hours comes from subtracting the speeds, which would only apply if they drove in the same direction.
-
Question 10
A student's average score on four tests is 85. What score does the student need on the fifth test to raise the average to 87?
Correct answer: D
An average of 87 on five tests requires a total of 5 × 87 = 435 points. The first four tests total 4 × 85 = 340, so the fifth score must be 435 − 340 = 95. Scoring 89 would raise the average only to 85.8.
-
Question 11
A generator uses 34 gallon of fuel per hour. How many hours will 12 gallons of fuel last?
Correct answer: D
Divide the fuel by the hourly use: 12 ÷ 3/4 = 12 × 4/3 = 16 hours. The answer 9 hours comes from multiplying 12 by 3/4 instead of dividing.
-
Question 12
A group of 250 people is going on a field trip. Each bus holds 44 passengers. What is the smallest number of buses needed so that everyone has a seat?
Correct answer: C
250 ÷ 44 ≈ 5.7, so 5 buses would carry only 220 people and leave 30 without a seat. You must round up to 6 buses.
Questions you leave blank are not counted as wrong.
More Arithmetic Reasoning tests
Arithmetic ReasoningASVAB Arithmetic Reasoning Practice Test 2Word Problems 215 questions18 min Arithmetic ReasoningASVAB Arithmetic Reasoning Practice Test 3: Percents, Ratios and Unit RatesPercents, Ratios and Unit Rates10 questions15 minArithmetic ReasoningASVAB Arithmetic Reasoning Practice Test 4: Speed, Work, Averages and MeasurementSpeed, Work, Averages and Measurement10 questions15 min