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## Official Guide Explanation:Data Sufficiency #D42

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.

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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