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## Official Guide Explanation:Data Sufficiency #148

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: 148
Page: 286
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Algebra > Linear Equations-Two Unk >

Explanation: The figure in this problem doesn't have any useful geometric characteristics (for instance, a right angle), so all we can do is try to find x.

Statement (1) is insufficient. Any of the four sides could be 120 meters. That could mean that x = 120, x + 60 = 120, or 3x = 120. All three options would give us different answers.

Statement (2) is sufficient. Since there are only two sides that are equal, the phrase "each of the two shortest sides" must refer to x. Since 3x is three times as long as x, it can't be the side that is twice as long. By process of elimination, x + 60 must be twice as long as x:

x + 60 = 2x

60 = x

We have the value of x, and we can find the total distance around the path. Choice (B) is correct.

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