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## Official Guide Explanation:Data Sufficiency #45

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: 45
Page: 156
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Since p and q are positive integers and pq = 24, p and q both must be positive factors of 24. Statement (1) is insufficient. If ((q)/6) is an integer, q must be a multiple of 6. There are 3 factors of 24 that are also multiples of 6: 6, 12, and 24, so there are 3 possible values of p.

Statement (2) is also insufficient: if ((p)/2) is an integer, p must be a multiple of 2. There are several factors of 24 that are also multiples of 2: 2, 4, 6, 8, 12, and 24.

Taken together, the statements are still insufficient. If p = 2 and q = 12, pq = 24 and both statements are true; also, if p = 4 and q = 6, pq = 24 and both statements are true. Since there are multiple possible values of p, choice (E) is correct.

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