Two line l and k intersect at a point (4, 3). Is the product of their slopes -1?
(1) x intercepts of line l and k are positive
(2) y intercept of line l and k are negative
Coordinate Geometry
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I believe that the question stem should read as follows.
Note the change in red:
Statement 1: The product of the x-intercepts of line L and K is positive.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:
K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
INSUFFICIENT.
Statement 2: The product of the y-intercepts of line L and k is negative.
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative:
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
INSUFFICIENT.
Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both x-intercepts be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, which does not satisfy statement 2:
Thus, both x-intercepts must be positive.
Statement 2 requires that one of the y-intercepts be positive, the other negative.
A positive x-intercept and a positive y-intercept yields a negative slope.
A positive x-intercept and a negative y-intercept yields a positive slope.
See below:
Thus, the product of the slopes must be negative.
SUFFICIENT.
The correct answer is C.
Note the change in red:
Don't solve. Draw.In the XY-coordinate plane, line L and line K intersect at the point (4, 3). Is the product of their slopes negative?
(1) The product of the x-intercepts of line L and K is positive.
(2) The product of the y-intercepts of line L and k is negative.
Statement 1: The product of the x-intercepts of line L and K is positive.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:
K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
INSUFFICIENT.
Statement 2: The product of the y-intercepts of line L and k is negative.
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative:
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
INSUFFICIENT.
Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both x-intercepts be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, which does not satisfy statement 2:
Thus, both x-intercepts must be positive.
Statement 2 requires that one of the y-intercepts be positive, the other negative.
A positive x-intercept and a positive y-intercept yields a negative slope.
A positive x-intercept and a negative y-intercept yields a positive slope.
See below:
Thus, the product of the slopes must be negative.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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