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Official Guide Explanation:Problem Solving #105

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: 105
Page: 75
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Linear Equations-Two Unk >
Category 2: Algebra > Simplifying Algebraic Expressions >

Explanation: Given the number of variables in this question, and the complex relationships between them, this is a great example to assign values to the variables. First, say that s = 10 and r = 2. If p is halfway between r and s, it's halfway been 10 and 2, or ((10 + 2)/2) = (12/2) = 6. If t is halfway between p and r, it's halfway between 6 and 2, or ((6 + 2)/2) = (8/2) = 4. Then, plug all of those values into the fraction ((s - t)/(t - r)):

((10 - 4)/(4 - 2)) = (6/2) = 3, choice (D).

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