Official Guide Explanation:
Data Sufficiency #100

 

 

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.

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Solution and Metadata

Question: 100
Page: 160
Difficulty: 5 (Moderate)
Category 1: Algebra > Exponents >
Category 2: Algebra > Equations >

Explanation: To answer the question, you need either the specific values of x and y or the values of xy and (x + y). Since you are given the value of xy, the second option requires only the value of (x + y).

Statement (1) is insufficient: with one more equation involving x and y, you can substitute x - y = 5 into the initial equation. Rewrite it as x = y + 5, and plug in: (y + 5)y= - 6, or y2 + 5y - 6 = 0. That'll have two possible values of y, so we can't find a specific value of either x or y. Statement (2) is also sufficient: it's another equation with x and y. Since xy= - 6 and xy2 = 18, you can substitute the first equation into the second: (-6)y = 18, or y= - 3. Choice (B) is correct.

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