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## Official Guide Explanation:Problem Solving #75

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: 75
Page: 71
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Other >

Explanation: This question looks like the sort of problem in which you write out the two statements algebraically, then solve for the variables. However, there are three variables instead of two, and rather than selecting from five numerical answers, you're asked to evaluate the truth of three statements. Let's look at each one in turn:

I.    If Rose is currently twice as old as Sam, she won't be in four years. If R = 20 and S = 10, in four years they'll be 24 and 14.

II.    If Sam is currently three years younger than Trina, that will never change. In four years, the relationship will still be the same: if S = 10 and T = 13, in four years they'll be 14 and 17.

III.    If Rose is to be older than Trina in four years, she'd have to be older than Trina now. In the examples given above, that's the case: R = 20 and T =13. However, be wary of relationships drawn from a mishmash of addition and multiplication. If R = 4 and S = 2, T = 5, so this isn't necessarily true.

Thus, the only statement that must be true is II, so choice (B) is correct.

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