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## Official Guide Explanation:Data Sufficiency #99

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: 99
Page: 281
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Linear Equations-Two Unk >

Explanation: Before jumping into the statements, make sure you understand the restrictions. Each of the numbers 1, 2, and 3 will appear in the table exactly 3 times, and not more than once in any row or column.

Statement (1) is sufficient. If v + z = 6, v and z must both be 3. That means that no variable in the same row or column with v or z can be 3. That eliminates everything in the middle row, the right - hand row, the middle column, and the bottom column. The only remaining number that could be equal to 3 is r. Since 3 must appear in the table three times, r must be three.

Statement (2) is also sufficient. s and t, and u and x must represent pairs of different numbers. For instance, s and t cannot both be 2. Thus, if the sum of the four numbers is to be 6, the sum of each pair must be 3, and the only way each pair can sum to 3 is if one of each pair is 1 and the other is 2. For instance s = 1, t = 2, u = 1, x = 3. Since those are the numbers that share a row and a column with r, r must be 3. Choice (D) is correct.

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