Official Guide Explanation:
Problem Solving #122




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Solution and Metadata

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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