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## Official Guide Explanation:Data Sufficiency #115

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 115
Page: 161
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Statement (1) is insufficient: if n is a multiple of 4, it could be 12 (not a multiple of 24) or 48 (a multiple of 24). Statement (2) is also insufficient: if n is a multiple of 6, it could be 12 (not a multiple of 24) or 48 (a multiple of 24).

Taken together, the statements are still insufficient. The least common multiple of 4 and 6 is 12, so the statements together imply that n must be a multiple of 12. If n is a multiple of 12, it might be a multiple of 24, but it's not a sure thing. Choice (E) is correct.

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