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## Official Guide Explanation:Problem Solving #D13

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: D13
Page: 22
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Fractions >
Category 2: Arithmetic > Properties of Integers > Remainder

Explanation: There are an infinite number of possible remainders given the decimal result of 64.12, but that result does limit what those remainders can be. When s is divided by t, the quotient is 64, and the fractional part of the answer is something equal to (12/100). The numerator of that fraction is the remainder, and the denominator is equal to t. A remainder is always an integer, and we know that t is a positive, integer, so the numerator and denominator must both be integers.

Simplify that (12/100) as much as possible, and the result is (3/25). If the numbers get any smaller, they are no longer integers. Thus, the remainder could be 3. 3 isn't an answer, but since we know that 3 is the smallest possible remainder, we can recognize that any multiple of 3 may also be the remainder. For instance, if t is 50, the remainder is 6. If t is 100, the remainder is 12. Any multiple of 3 is acceptable. Thus, choice (E) is correct.

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