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## Official Guide Explanation:Data Sufficiency #90

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: 90
Page: 280
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Fractions >
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Before looking at the statements, simplify the given equation by multiplying both sides by 12:

((k)/6) + ((m)/4) = ((t)/12)

2k + 3m = t

Statement (1) is sufficient. If k is a multiple of 3, then 2k is a multiple of 3. Because m is an integer, 3m is a multiple of 3. Since both 2k and 3m are multiples of 3, their sum, t, is also a multiple of 3. Thus, t and 12 have a common factor greater than 1--that common factor is 3.

Statement (2) is insufficient. Knowing that m is a multiple of 3 tells us that 3m is a multiple of 9. There's no evidence that 2k and 3m have any factors in common, so we don't know that t has any specific factors. For instance, if k = 1 and m = 3, t = 11, so the answer would be "no." However, if k = 3 and m = 3, t = 15, so the answer would be "yes." Choice (A) is correct.

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