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Official Guide Explanation:Problem Solving #51

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: 51
Page: 159
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: There are a couple of ways to do this. The simplest way is to add rt[7]+ rt[7]to get 2 rt[7]. Then square it, remembering to square each of the two components: (2 rt[7])2 = (2)2( rt[7])2 = 4(7) = 28, choice (C).

The other alternative is to view this the way you would a factored binomial. You should know, for general GMAT purposes, that (x + y)2 = x2 + 2xy + y2. In this case, both x and y are rt[7]. Thus, x2 + 2xy + y2 = 7 + 2(7) + 7 = 28. If you immediate recognize the relationship between a question like this and its algebraic counterpart, this method is probably faster. If you don't, remember to watch for them; as questions get harder, relationships such as that one can be the key to doing the problem in a reasonable amount of time.

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