ASVAB Arithmetic Reasoning Practice: Inequalities

The Arithmetic Reasoning subtest on the ASVAB will contain some inequality questions. You can identify them because they contain phrases like "at least" and "less than or equal to."

Practice questions

1. Express mathematically: The product of x and y is greater than or equal to the quotient of b and c.

   

2. Benjamin works 15 hours per week to be eligible for a work-study program. In order to keep up his grades, Benjamin needs to study at least 12 more hours per week than he works. What is the minimum number of hours Benjamin needs to study to keep up his grades?

   A. 15 hours B. 28.5 hours C. 27 hours D. 30 hours

Answers and explanations

1. The correct answer is Choice (C).

   When you see product in a word problem, you're dealing with multiplication; when you see quotient, you're dealing with division. You express the relationship in this problem with an inequality, because it uses the phrase "is greater than or equal to":

   

2. The correct answer is Choice (C).

   You can express Benjamin's situation with an inequality, letting h represent the number of hours he needs to study. The problem says "the minimum number," so your inequality will look like this:

   

   Solve the inequality just as you would any other:

   

   That tells you Benjamin needs to study at least 27 hours each week. (You can also use your own arithmetic reasoning to add 15 and 12 — the number of hours Benjamin has to work, plus the number of hours he has to study — in your head to arrive at the correct answer.)