Official Guide Explanation:
Data Sufficiency #90




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Solution and Metadata

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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