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Official Guide Explanation:
Data Sufficiency #82
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.
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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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