Official Guide Explanation:
Data Sufficiency #150




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Solution and Metadata

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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