Official Guide Explanation:
Data Sufficiency #82




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Solution and Metadata

Question: 82
Page: 280
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: If x is a multiple of 6 and y is a multiple of 14, xy must be a multiple of 6(14) = 84. If xy is to be a multiple of 105, it must have factors of 3, 5, and 7. 84 has factors of 3 and 7, but not of 5. To establish whether xy is a multiple of 105, we must either learn that either x or y is a multiple of 5 (in which case the answer is "yes"), or that neither variable is a multiple of 5 (in which case the answer is "no").

Statement (1) is insufficient. Without redoing all the calculations, it's clear that this doesn't tell us whether x is a multiple of 5, and it says nothing about y.

Statement (2) is sufficient. If y is a multiple of 25, it is a multiple of 5. Thus, xy is a multiple of 5, and since we already know it is a multiple of 3 and 7, it is a multiple of 3(5)(7) = 105. Choice (B) is correct.

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