Official Guide Explanation:
Problem Solving #106

 

 

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: 106
Page: 75
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Real Numbers >
Category 2: Algebra > Equations >

Explanation: Trying to simplify the equation x2 = xy raises an important point. Generally, you can divide both sides by x, leaving x = y. However, this question specifies that x and y are different integers, so x ≠ y. Whenever you divide both sides of an equation by a variable, there's always the possibility that the variable is 0. (If both sides are multiplied by zero, both sides are equal to zero, and they are equal.) In this case, if x = 0, y could be any number. So, if x2 = xy and x ≠ y, it must be the case that x = 0. Now, we can look at the statements:

I.    Yes, we've established that x = 0.

II.    This cannot be true: if x = 0 and x ≠ y, y cannot be 0.

III.    Since x = 0, if x= - y, then y = 0, and we've just seen that y cannot be 0.

I is the only statement that must be true, so the correct choice is (A).

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