Official Guide Explanation:
Problem Solving #D13

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Solution and Metadata

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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