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## Official Guide Explanation:Data Sufficiency #88

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: 88
Page: 159
Difficulty: 5 (Moderate)
Category 1: Geometry > Triangles > Multiple figures
Category 2: Geometry > Circles > Multiple figures
Category 3: Arithmetic > Ratio and Proportion >

Explanation: Statement (1) is sufficient: if the ratio of a side of S to a side of T is 4:5, we can say that a side of S is 4x, and a side of T is 5x. Then, the perimeter of S is 4(4x) = 16x, and the perimeter of T is 3(5x) = 15x. So, the perimeter of S is greater.

Statement (2) is insufficient: given the sum of one side of each, the lengths could be anything: a side of T could be 17 and a side of S 1, or the other way around. Choice (A) is correct.

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