Official Guide Explanation:
Data Sufficiency #168




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Solution and Metadata

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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