x-intercept

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grandh01: Master | Next Rank: 500 Posts; Posts: 265; Joined: Tue Jul 03, 2012 11:04 pmFollowed by: 6 members

by grandh01 » Tue Sep 25, 2012 9:13 pm

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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Source: Beat The GMAT — Data Sufficiency | Tue Sep 25, 2012 9:13 pm

anuprajan5: Master | Next Rank: 500 Posts; Posts: 279; Joined: Mon Jun 25, 2012 10:56 pmFollowed by: 10 members; Thanked: 60 times

by anuprajan5 » Wed Sep 26, 2012 7:48 am

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

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Sep 27, 2012 1:01 pm

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

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.

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

ianstewartgmat.com

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