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## Official Guide Explanation:Data Sufficiency #168

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th 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: 168
Page: 288
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Fractions >
Category 2: Algebra > Simplifying Algebraic Expressions >

Explanation: Notice that there's a t - x on both the top and bottom of the fraction. Take advantage of things like that. Just as you can simplify ((x + y)/3) to ((x)/3) + ((y)/3), we can do the following:

((2t + t - x)/(t - x))

= ((2t)/(t - x)) + ((t - x)/(t - x))

= ((2t)/(t - x)) + 1

Without looking at the statements, we don't know that this version will be any more useful than the original, but it gives us more options and a simpler fraction to work with.

Statement (1) is sufficient. The simplification paid off. If ((2t)/(t - x)) = 3, the value of the original fraction (which is equivalent to ((2t)/(t - x)) + 1) is 3 + 1 = 4.

Statement (2) is not sufficient. In either the original version of the fraction or our simplified version, it gives us the denominator. But in each case, we would still need the value of 2t:

((2t)/(t - x)) + 1 = ((2t)/3) + 1

We don't get a number, so it's not enough information. Choice (A) is correct.

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