Official Guide Explanation:
Problem Solving #D23




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Solution and Metadata

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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