Official Guide Explanation:
Data Sufficiency #45

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Solution and Metadata

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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