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## Official Guide Explanation:Problem Solving #176

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: 176
Page: 177
Difficulty: 5 (Moderate)
Category 1: Algebra > Equations >
Category 2: Algebra > Linear Equations-One Unk >
Category 3: Arithmetic > Fractions >

Explanation: In the first two roman numerals, you can ignore the constants: regardless of what happens to x, -5 and 1 won't change. So, I increases: as x gets larger, so does 2x. II is tricker. As x gets bigger, (1/(x)) gets smaller, but as (1/(x)) gets smaller, -(1/(x)) gets bigger, so II increases. III is also somewhat involved, but we don't have to do it: if I and II increase, the only possible answer choice is (C).

For the sake of completeness, here's how you can tell that III does not increase. First, forget about the fraction and focus on x2-x. As x increases, x2 increases, while x does not. But x2 increases by a greater amount--1662-1652 is greater than 166 - 165. So, x2-x increases. However, since III is the inverse of that, knowing that x2-x increases tells us that (1/(x2-x)) decreases.

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