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## Official Guide Explanation:Problem Solving #157

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.

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: 157
Page: 83
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Triangles > Length of sides

Explanation: Given that it is a right triangle, we know that the two legs--that is, the two shortest sides, since the hypotenuse must be the longest--are the base and height. Thus, we're dealing with b and h in the formula

1 = (1/2)bh

2 = bh

If base and height were equal, each one would be rt[2]. However, we're looking for the larger of the two legs, the side that is the middle length of the three sides. So y must be greater than rt[2] and up to infinity. (The triangle could be very, very skinny.) Because there's no reason y can't be very large, look for the biggest choice. In this case, it's (A): y> rt[2].

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