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## Official Guide Explanation:Problem Solving #92

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: 92
Page: 73
Difficulty: 5 (Moderate)
Category 1: Algebra > Inequalities > other
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: If you're given an inequality and you need to find what it implies about another variable, see what happens when the first variable is at the limit of its inequality. In this case, that means finding out what happens in the equation, when b = 2.

2x - 3(2) = 0

2x = 6

x = 3

That doesn't mean that (C) is right (necessarily), just that 3 is the boundary line. So (C), (D), or (E) must be right. To find out which one, use another number for b that fits the constraints of the inequality, such as b = 1:

2x - 3(1) = 0

2x = 3

x = (3/2)

Since x could be equal to (3/2), the inequality must allow for x to be less than 3, so (D) must be correct.

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