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## Official Guide Explanation:Data Sufficiency #95

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: 95
Page: 281
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Arithmetic > Real Numbers >

Explanation: Statement (1) is insufficient. If rs = 1, rst will be 1 if t equals 1. Since we don't know whether t is 1, we don't know whether rst = 1. Statement (2) is also insufficient: if st = 1, rst will be 1 if r is 1. Since we don't know whether r is 1, we don't know whether rst = 1.

Taken together, the statements are still insufficient. rs = 1 and st = 1, which means that r = t. So, we can put all three variables in terms of r: s = (1/(r)), and t = r. We can then rewrite the question: is (r)((1/(r)))(r) = 1, or "Is r = 1?" Neither statement says anything about a specific variable, so we don't know. The correct choice is (E).

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