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## Official Guide Explanation:Problem Solving #D23

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: D23
Page: 23
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: If x is a multiple of 4 and y is a multiple of 6, xy must be a multiple of 24. Another way to think of it is that x = 4i, where i is an integer, and y = 6j, where j is an integer. xy, then, is equal to 24ij, where ij is an integer--perhaps just 1, but also possibly any other integer.

Thus, xy must be a multiple of 24, as well as all factors of 24. 8 and 12 are factors of 24, but 18 is not, so choice (B) is correct.

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