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## Official Guide Explanation:

Problem Solving #42

**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.

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

**Solution and Metadata**

**Question****: 42**

Page: 158

Difficulty: **4** (Moderately Easy)

Category 1: Algebra > Symbolism >

**Explanation:** It looks unorthodox, but this is a fairly typical symbolism problem. Given the matrix (really just an equation, though not a typical representation of one), we're told that the value of the matrix is the product of the upper left and lower right numbers (a and d) minus the product of the other two numbers (b and c).

Thus, given the matrix in the question, the value is:

(3)(4) - (5)(-2) = 12 - (-10) = 12 + 10 = 22, choice (E).

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