Brent@GMATPrepNow wrote:In xy-coordinate plane, lines j and k intersect at the point (5, 0). If both lines have defined slopes, is the y-intercept of line j greater than the y-intercept of line k?
1) The slope of line k is greater than the slope of line j.
2) Line j has a negative slope
Alternate approach:
Statement 1:
According to the prompt, both lines include (5, 0).
Let (0, K) = the y-intercept of line k and (0, J) = the y-intercept of line j.
Thus:
Slope of line k = (y₂ - y�)/(x₂ - x�) = (K-0)/(0-5) = K/-5.
Slope of line j = (y₂ - y�)/(x₂ - x�) = (J-0)/(0-5) = J/-5.
Since the slope of line k is greater than the slope of line j, we get:
K/-5 > J/-5.
Multiplying each side by -5 and flipping the inequality symbol, we get:
K < J.
Since J>K, the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
Here, the y-intercept of line k can be ANY VALUE.
Thus, it cannot be determined whether line j has a greater y-intercept than line k.
INSUFFICIENT.
The correct answer is
A.
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