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Official Guide Explanation:Data Sufficiency #94

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: 94
Page: 281
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Slope
Category 2: Geometry > Coordinate Geometry > Other

Explanation: Given the equation of a line in standard form (as it is given to us in this question), the slope is m. That's what we need to answer the question.

Statement (1) is sufficient. Parallel lines have equal slopes. The line in (1) is also given in point - slope form, only the slope is (1 - m) and the y - intercept is b + 1 . We can ignore the intercept since we only care about the slope. Since the slopes of this line and the one in the question are the same, we can set them equal to each other:

m = 1 - m

2m = 1

m = (1/2)

Statement (2) is insufficient. To say that a line intersects another line tells you only one thing: They are not parallel. So, the only relevant information is that the line we care about passes through the point (2,7). If we knew another point as well, we could calculate the slope. However, with just one point, we can't. Choice (A) is correct.

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