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## Official Guide Explanation:Problem Solving #152

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 152
Page: 82
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Algebra > Absolute Value >

Explanation: First, consider the number and range of possibilities for the second equation. The absolute value of y must be less than or equal to 12, so if we're looking only for pairs of values including two integers, we should start by considering every integer for y between -12 and 12, inclusive.

Try a few of the possible values to see what might work. If y = 12, then:

2x + 12 = 12

2x = 0

x = 0

That's acceptable.

If y = 11:

2x + 11 = 12

2x = 1

x = (1/2)

Not acceptable. The same applies for negatives. If y= - 12, 2x = 24, and x is an integer. But if y= - 11, 2x = 23, and x is not an integer.

The rule, then, is that all even values for y result in an integer value for x. Thus, we need to know how many even values are acceptable for y. Between -12 and 12, we have:

-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, and 12

Don't forget zero, and you have 13 values, choice (D).

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