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## Official Guide Explanation:

Problem Solving #41

**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.

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**Solution and Metadata**

**Question****: 41**

Page: 158

Difficulty: **5** (Moderate)

Category 1: Algebra > Solving Quadratic Equations > other

Category 2: Algebra > Solving Equations by Factoring >

**Explanation:** Whenever you see something like a biominal, turn it into something you can work with. In this case, x^{2} + 3x + k = 10 can be better viewed as x^{2} + 3x + (k - 10) = 0. Since one of the solutions is 4, one of the factors must be (x - 4). Putting all of this together, we know that (x - 4)(x + q) = x^{2} + 3x + (k - 10). Because -4 and q must sum to 3, q must be 7. If x + q is one of the factors, -q is the other solution, so the correct answer is -7, choice (A).

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