In the xy-plane, if line l has negative slope and passes through
the point (-4, q), is the x-intercept of line l positive?
(1) q < 0
(2) The slope of line l is -4
OA IS A
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x-intercept
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anuprajan5
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Hi,
My solution looks something like this:
The question is if the x intercept is positive
To determine the x-intercept y = 0. Therefore mx+c = 0. Therefore x = -c/m
Rephrased the question asks if -c/m >0
y = mx+c and since it passes through the point(-4,q), this would translate to
q = -4m +c which gives us that c = q+4m
Therefore -c/m = -(q+4m)/m
Statement 1 : q <0
This means that q is negative and m is also negative (per question). Therefore -c/m = -(q+4m)/m will also be negative. Sufficient.
Statement 2: Slope of line is -4.
Therefore -c/m = -(q-16)/-4 which gives us (q-16)/4. Since this does not give us any information on q, we cannot conclude if the expression will be positive or negative. Hence insufficient.
Hence the answer is A
My solution looks something like this:
The question is if the x intercept is positive
To determine the x-intercept y = 0. Therefore mx+c = 0. Therefore x = -c/m
Rephrased the question asks if -c/m >0
y = mx+c and since it passes through the point(-4,q), this would translate to
q = -4m +c which gives us that c = q+4m
Therefore -c/m = -(q+4m)/m
Statement 1 : q <0
This means that q is negative and m is also negative (per question). Therefore -c/m = -(q+4m)/m will also be negative. Sufficient.
Statement 2: Slope of line is -4.
Therefore -c/m = -(q-16)/-4 which gives us (q-16)/4. Since this does not give us any information on q, we cannot conclude if the expression will be positive or negative. Hence insufficient.
Hence the answer is A
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Ian Stewart
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These questions are a lot easier to answer just by drawing scenarios on the coordinate plane, but since we can't do that so easily here, I'll do my best to explain in words.grandh01 wrote:In the xy-plane, if line l has negative slope and passes through
the point (-4, q), is the x-intercept of line l positive?
(1) q < 0
(2) The slope of line l is -4
OA IS A
We know (-4, q) is on our line. If, from Statement 1, q is negative, that means that at x = -4, the line is somewhere below the x-axis. Since the slope of the line is negative, the line falls as it moves to the right, or equivalently rises as you move to the left. So its x-intercept is somewhere to the left of x = -4, and thus must be negative, and Statement 1 is sufficient.
Statement 2 is not sufficient, since all it tells us is that our line is falling quite steeply; it could have any x-intercept at all.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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