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Official Guide Explanation:Problem Solving #227

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: 227
Page: 185
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Solving Quadratic Equations > Difference of Squares
Category 2: Algebra > Solving Quadratic Equations > Squares
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: 2xy may look familiar to you as a common middle term in a squared binomial, as in (x - y)2 = x2-2xy + y2. To come up with 2xy from the equations given, square each one, resulting in the following:

x2 + 2xy + y2 = a2

x2-2xy + y2 = b2

To isolate 2xy, subtract the second equation from the first one, resulting in:

4xy = a2-b2

2xy = ((a2-b2)/2), choice (A).

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