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## Official Guide Explanation:Problem Solving #88

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.

Question: 88
Page: 164
Difficulty: 5 (Moderate)
Category 1: Geometry > Coordinate Geometry > Slope
Category 2: Algebra > Linear Equations-One Unk >

Explanation: Given the equation of the line and two points, you can create two equations, one for each point. By plugging in the first point into the equation, you get:

a = 3b - 7

Plug in the second, and you get:

(a + 3) = 3(b + k) - 7

a + 3 = 3b + 3k - 7

Line up the two equations so that they can be easily combined by subtraction:

a + 3 = 3b - 7+ 3k

-    a = 3b - 7

=     3 = 3k

Finally, simplify: k = 1, choice (D).

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