Coordinate geometry-DS- Question

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Coordinate geometry-DS- Question

by gmat_thingie » Sat Nov 22, 2014 12:25 am
Line L1 has a slope A and Line L2 has the slope B. Is A greater than B?

1. The y intercept of L1 is greater than the Y intercept of line L2.
2. L1 and L2 intersect at point Q (5,9)

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by GMATGuruNY » Sat Nov 22, 2014 4:01 am
gmat_thingie wrote:Line L1 has a slope A and Line L2 has the slope B. Is A greater than B?

1. The y intercept of L1 is greater than the Y intercept of line L2.
2. L1 and L2 intersect at point Q (5,9)
Neither statement alone tells us anything about the slopes of L1 and L2.

Statements combined:
Both lines include point (5, 9).

Case 1: y-intercept of L1 = (0, 1), y-intercept of L2 = (0, 0).
A = Slope of L1 = (y₂ - y�)/(x₂ - x�) = (1-9)/(0-5) = 8/5.
B = Slope of L2 = (y₂ - y�)/(x₂ - x�) = (0-9)/(0-5) = 9/5.
In this case, A<B.

Case 2: y-intercept of L1 = (0, -1), y-intercept of L2 = (0, -11).
A = Slope of L1 = (y₂ - y�)/(x₂ - x�) = (-1-9)/(0-5) = 2.
B = Slope of L2 = (y₂ - y�)/(x₂ - x�) = (-11-9)/(0-5) = 4.
In this case, A<B.

The cases above illustrate that -- given the constraints that L1 has a greater y-intercept and that both lines include point (5, 9) -- the slope of L1 must be LESS than the slope of L2.
SUFFICIENT.

The correct answer is C.
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