Official Guide Explanation:
Problem Solving #72




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Solution and Metadata

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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