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Please help to solve this Tough DS question.

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Please help to solve this Tough DS question.

by GaneshMalkar » Mon May 27, 2013 5:53 am
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-intersects of lines L and K is positive.
(2) The product of the y-intersects of lines L and K is negative.


Source - Tough 700 Questionnaire.

OA - C


I searched this question on this forum and found that

L = a1x + b1
K = a2x + b2

Slope L : -b1/a1
Slope K : -b2/a2

But the slope form of the equation is y = mx + c, so the above equation should have slope as a1 only and not -b1/a1


If the equation is in standard form Ax + By + C = 0 then y = -A/Bx - C/A
then the slope is -A/b and y-intercept = - C/A


So L = a1x + b1 is in which form?
If you cant explain it simply you dont understand it well enough!!!
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Source: — Data Sufficiency |
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by sanjayism » Mon May 27, 2013 6:34 am
Lets us write the equation of line in intercept form.

equation of line L is x/a + y/b = 1
equation of line K is x/c + y/d = 1


slope of line L is =-(b/a)
slope of line K is =-(d/c)

product of slopes = -(b/a) * -(d/c)= bd/ac

we have dertermine whether bd/ac is negative or not.


statment1 = a*c >0

from above statment it is not possible to say that bd/ac is nagative. it will depends on bd, if bd is positive then bd/ac is positive and vice versa.

so S1 is not sufficint to decide the answer.

similarlly , SM2 is not sufficient to answer the question clearly. if bd is negative then it is not possible to say that bd/ac is nagative. it will depends on ac, if ac is positive then bd/ac is positive and vice versa.

if both statment consider jointly then it can be answered clearly.

SM1 ac>0
SM2 bd<0

so product of slope i.e. bd/ac <0

so answer is c
kumar sanjay
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by GMATGuruNY » Mon May 27, 2013 7:21 pm
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.
Don't solve. Draw.

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:
Image

K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
Image
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:
Image

K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
Image
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:
Image

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:
Image
Thus, the product of the slopes must be negative.
SUFFICIENT.

The correct answer is C.
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by GaneshMalkar » Tue May 28, 2013 8:56 am
Thank you very much Mitch.
Can you please confirm my below understanding if it is right or wrong?

1. If a line in a plane is directed in a north-east direction it will have a positive slope.
2. if a line in a plane is directed in a south-east direction it will have a negative slope.
3. If a line is parallel to y-axis the slope is not defined.
4. If a line is parallel to x-axis the slope is zero.


So in this way, we have evaluated the four cases in the statement 1 and statement 2 will not poise any problem correct?
If you cant explain it simply you dont understand it well enough!!!
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