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## Official Guide Explanation:Data Sufficiency #150

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: 150
Page: 286
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Fractions >
Category 2: Algebra > Equations >
Category 3: Arithmetic > Ratio and Proportion >

Explanation: So that it will be easier to spot a sufficient statement, first simplify the equation:

S = (((2/(n)))/((1/(x)) + (2/(3x)))) = (((2/(n)))/((3/(3x)) + (2/(3x)))) = (((2/(n)))/(((3 + 2)/(3x)))) = (((2/(n)))/((5/(3x)))) = ((2/(n)))(((3x)/5)) = ((6x)/(5n))

In other words, to find the value of S, you need the ratio ((x)/(n)). Statement (1) is sufficient: divide both sides by 2, and ((x)/(n)) = 2. Statement (2) is insufficient: it doesn't provide a ratio or a value of x, so it would be impossible to find S. The correct choice is (A).

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