Official Guide Explanation:
Data Sufficiency #D39

Background

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Solution and Metadata

Question: D39
Page: 25
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Slope
Category 2: Geometry > Coordinate Geometry > Other

Explanation: Knowing that a line passes through the point (-5,r) isn't very helpful--almost every point has a point somewhere with an x - coordinate of -5. Before attacking the statements, think about lines with a negative slopes, and what would be required for such a line to have a positive x - intercept. A line with a negative slope moves down and to the right (or up and to the left, depending on how you think about it). If such a line passes through the x - axis when x is positive, one way to think about it is that it starts in the upper left quadrant, moves into the upper right quadrant after passing through the y - axis, then passes into the lower right quadrant after passing through the x - axis.

Statement (1) is insufficient. Knowing the slope tells us the "tilt" or angle of the line, but nothing about the intercepts of the line.

Statement (2) is also insufficient. In the scenario described above, r must be positive. (When the line is to the left of the origin, the y value must be positive.) However, it's possible that r is positive and the x - intercept is negative. If the point is, say, (-5, - 1) and the line moves sharply downward, the x - intercept will be negative.

Taken together, the statements are insufficient. I've already described the situation in which the answer would be "no"--if r = 1 and the slope is -5 (that is, it moves sharply downward), the x - intercept will be negative. However, if r is sufficiently great (say, r = 1000--there's no limit on how great r can be), even a line moving sharply downward will have positive x- and y - intercepts. Choice (E) is correct.

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