Official Guide Explanation:
Data Sufficiency #88

Background

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Solution and Metadata

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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