Official Guide Explanation:
Problem Solving #174




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Solution and Metadata

Question: 174
Page: 85
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Symbolism >
Category 2: Arithmetic > Properties of Integers > Other
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: This is an excellent question to guess and check on. First, ignore (A) because the question requires that each symbol stand for a different digit: two of them can't both be 1. Look for the choices in which the second digit of the answer choice is equal to the first and third digits of the product:

(B): 12(21) = 252 The hundreds and units digits are the same, but they aren't the same as the tens digit in the answer choice.

(C): 13(31) = 403 The hundreds digit is wrong. Note that this also eliminates choice (E); 403 is also the product of 31(13).

(D): 21(12) = 252 The hundreds and units digits are the same, and they match the tens digit in the answer choice. This is correct.

(D) must be correct.

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