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## Official Guide Explanation:Problem Solving #72

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: 72
Page: 162
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: The problem is basically explaining that the number of students in the class is divisible by both 8 and 12. Since we're looking for the smallest possible number, we're really interested in a lowest common multiple. To find a least common multiple, find the largest common factor between the numbers (4), divide one of the numbers by that factor, and multiply the result by the other number. In this case, divide 8 by 4, resulting in 2, then multiply 2 by 12 to get a total of 24, choice (B).

Alternatively, with small numbers like these, you can always start with the smallest number and simply test each one to see whether it is a multiple of both 8 and 12.

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