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Official Guide Explanation:
Problem Solving #215
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.
Solution and Metadata
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Linear Equations-One Unk >
Category 2: Algebra > Simplifying Algebraic Expressions >
Category 3: Arithmetic > Fractions >
Explanation: This is an excellent problem on which to guess and check. Because the denominators are x, x + 1, and x + 4, choices (A), (B), and (E) cannot be correct: they would result in zero in a denominator. So, there are really only two possible values of x to plug into the equation and test. Let's try (C):
(1/(-2)) - (1/((-2 + 1))) = (1/((-2 + 4)))
-(1/2) - (1/(-1)) = (1/2)
-(1/2) + 1 = (1/2)
That's right, so (C) must be the correct choice.
Alternatively, this question can be solved algebraically (but it's much more time consuming than the first method).
(1/(x)) - (1/(x + 1)) = (1/(x + 4))
((x + 1)/(x(x + 1))) - ((x)/(x(x + 1))) = (1/(x + 4))
((x + 1 - x)/(x2 + x)) = (1/(x + 4))
x + 4 = x2 + x
x2-4 = 0
x = \pm 2
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