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by sud21 » Sun Jan 22, 2012 11:19 pm
Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?
A. (2,3)
B. (5,7)
C. (4,2)
D. (4,-1)
E. (5, -1)
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by Anurag@Gurome » Sun Jan 22, 2012 11:26 pm
sud21 wrote:Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?
As the product of the intercepts of the line L with axis-x and axis-y is negative, the slope of L is positive.

Hence, if (a, b) is a point on L, then (b - 4)/(a - 1) > 0
Hence, (b - 4) and (a - 1) both must be of same sign, i.e. either (b > 4 and a > 1) or (b < 4 and a < 1)

Only for option B (b > 4 and a > 1)

The correct answer is B.
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by Anurag@Gurome » Sun Jan 22, 2012 11:31 pm
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by abdul_gmat » Mon Jan 23, 2012 7:28 am
Anurag@Gurome wrote:
sud21 wrote:Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?
As the product of the intercepts of the line L with axis-x and axis-y is negative, the slope of L is positive.

Hence, if (a, b) is a point on L, then (b - 4)/(a - 1) > 0
Hence, (b - 4) and (a - 1) both must be of same sign, i.e. either (b > 4 and a > 1) or (b < 4 and a < 1)

Only for option B (b > 4 and a > 1)

The correct answer is B.
Hi,
I'm missing some concept here. why should be the slope positive here ?
Thanks
Abdul
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by Anurag@Gurome » Mon Jan 23, 2012 7:39 am
abdul_gmat wrote:...why should be the slope positive here ?
Product of x and y intercepts of the line L is negative. Hence, the x and y intercepts of L are of opposite sign.

Now, slope of a line = -(y-intercept of the line)/(x-intercept of the line)

Hence, slope of L = -(y-intercept of L)/(x-intercept of L) > 0
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by GMATGuruNY » Tue Jan 24, 2012 8:00 pm
sud21 wrote:Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?
A. (2,3)
B. (5,7)
C. (4,2)
D. (4,-1)
E. (5, -1)
Many slope questions can be solved -- easily and efficiently -- by drawing:

Image

In order for the product of the x and y intercepts to be negative, line L must look like one of the two lines above.
The drawing shows that, of the points given in the answer choices, only (5,7) could be on one of the two lines.

The correct answer is B.
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by ArunangsuSahu » Wed Jan 25, 2012 12:03 pm
The line will pass through 1st, 3rd and 4th Quadrant.

So the points(a,b) on this line need to be in the following manner
1. a>1, b>4
2. a<1, b<4
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