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## Official Guide Explanation:Problem Solving #210

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: 210
Page: 182
Difficulty: 5 (Moderate)
Category 1: Geometry > Coordinate Geometry > Other

Explanation: A great way to check whether an equation represents a given line is to take one or two known points from the line and plug them into the equation to see if they work. For instance, one of the points on line l is (3,0), so check to see which of the answer choices work when x = 3 and y = 0.

(A) 2(3) - 3(0) = 6 - 0 = 6. Possible.

(B) 2(3) + 3(0) = 6 + 0 = 6. Possible.

(C) 3(3) + 2(0) = 9 + 0 = 9. Wrong.

(D) 2(3) - 3(0) = 6 - 0 = 6. Possible.

(E) 3(3) - 2(0) = 9 - 0 = 9. Wrong.

Now, use the other known point on line l, (0, 2), and try the remaining choices:

(A) 2(0) - 3(2) = 0 - 6= - 6. Wrong.

(B) 2(0) + 3(2) = 0 + 6 = 6. Possible.

(D) 3(0) - 2(2) = 0 - 4= - 4. Wrong.

Thus, only (B) works with both points, so it must be correct.

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