Official Guide Explanation:
Data Sufficiency #100




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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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