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## Official Guide Explanation:

Problem Solving #174

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**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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