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## Official Guide Explanation:Problem Solving #122

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: 122
Page: 77
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Other
Category 2: Algebra > Inequalities > other

Explanation: First, simplify the equation 2s = 2u + 2v. Divide each side by 2, resulting in s = u + v. Now evaluate the statements:

I.    Not only does s not have to equal u, they can't equal each other. If they did, v would equal 0, and each of the variables represents a positive integer.

II.    u can equal v; for instance, if u = 2, v = 2, and s = 4.

III.    Another way to phrase the equation is that "s is u greater than v." Since u is positive, then s is greater than v, so this statement is true.

III is the only one of the three that must be true, so the correct choice is (D).

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