Official Guide Explanation:
Problem Solving #227




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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.


Solution and Metadata

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).

Click here for the full list of GMAT OG12 explanations.


You should follow me on Twitter. While you're at it, take a moment to subscribe to GMAT Hacks via RSS or Email.

Total GMAT Math

The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises!
Click to read more.