Official Guide Explanation:
Data Sufficiency #D42

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Solution and Metadata

Question: D42
Page: 25
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: Statement (1) is insufficient. It tells us that k is a multiple of 15. It must have at least two prime factors, 3 and 5. It could have any other prime factors, up to an infinite number of them, but we only know for sure that it has two.

Statement (2) is also insufficient. By the same reasoning, we know that 2 and 5 are both prime factors of k. Again, it could have many other prime factors, but we only know of two of them.

Taken together, the statements are sufficient. We know that 2, 3, and 5 are prime factors of k, so k must have at least three different prime factors. Choice (C) is correct.

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