The folks who write the Arithmetic Reasoning subtest on the ASVAB have a soft spot for questions that ask you to express text as an equation. Luckily, you can look for key terms like these to help you write the equation:

Addition: look for terms like more, more than, sum, or increased

Subtraction: look for terms like minus, less, or less than

Multiplication: look for terms like times, of, twice, or product

Division: look for terms like quotient, divided by, half, or third

Equalities and inequalities: look for terms like equals, is, or is greater than or equal to

Practice questions

  1. Express as an equation: The product of two numbers is 75, and one of them is 15 more than the other.

    A. 75 = x(15x) B. 75 = x(x + 15) C. y = 75 – x(x + 15) D. Both A and B are correct

  2. Express as an equation: The reciprocal of a number is equal to the sum of two times the number and its opposite.


Answers and explanations

  1. The correct answer is Choice (B).

    The word product means that the problem involves multiplication, and when you see more than, you know you're adding. Therefore, you can express this equation this way:

    75 = x(x + 15)

    Here, one factor is x and the other factor is x + 15, and their product equals 75.

    There are several other ways to express the equation, but when you see a question like this on the ASVAB, it's often best to go through the answer choices to see which one fits instead of creating your own formula. (It's faster, too!)

  2. The correct answer is Choice (D).

    Let x be the variable and create an equation that looks like this:


    You can also simplify the equation so it looks like this:


    Therefore, both Choice (A) and Choice (C) are correct.

    Remember, when the ASVAB asks you to express an equation, key words tell you what to do. A reciprocal is the opposite of a number


About This Article

This article is from the book:

About the book author:

Angie Papple Johnston joined the U.S. Army in 2006 as a Chemical, Biological, Radiological, and Nuclear specialist, ready to tackle chemical weapons in a Level- A HAZMAT suit. She's currently the CBRN noncommissioned officer-in-charge of an aviation battalion in Washington, D.C.

This article can be found in the category: