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In the XY-coordinate plane, is the product of slopes

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Raxit85
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In the XY-coordinate plane, is the product of slopes [#permalink] New post   21 Nov 2019, 01:35
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56% (01:48) correct 44% (01:26) wrong based on 71 sessions
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In the XY-coordinate plane, is the product of slopes of line L and line K 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.
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C
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rajatchopra1994
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Re: In the XY-coordinate plane, is the product of slopes [#permalink] New post   21 Nov 2019, 03:35
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Raxit85 wrote:
In the XY-coordinate plane, is the product of slopes of line L and line K 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.



Explanation:

gmatbull Thanks, I still remember your answer for this type of question.

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Let M1 and M2 represent the gradients of lines K and L

(1)
from sketch (i), M1*M2 < 0
from sketch (ii), M1*M2 > 0
INSUFFICIENT

(2)
from sketch (i), M1*M2 < 0
from sketch (iii), M1*M2 > 0
INSUFFICIENT

Combining (1) and (2):
ONLY sketch i) satisfies --> SUFFICIENCY
option C is therefore correct

:please Pls provide kudos, if you find my explanation good enough :please
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intersecting lines K and L.docx [11.19 KiB]
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Re: In the XY-coordinate plane, is the product of slopes [#permalink] New post   18 Sep 2021, 07:51
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Raxit85 wrote:
In the XY-coordinate plane, is the product of slopes of line L and line K 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 slope of lines L and K could be anything. Insufficient.

Statement 2:

The slope of lines L and K could be anything. Insufficient.

Combined:

If we have two positive x-intercepts, lines L and K will have 1 positive slope and 1 negative slope.

If we have two negative x-intercepts, lines L and K will still have 1 positive slope and 1 negative slope.

Either way, the product of slopes is negative. Sufficient.

Ans: C
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Re: In the XY-coordinate plane, is the product of slopes [#permalink] New post   18 Oct 2021, 23:45
Raxit85 wrote:
In the XY-coordinate plane, is the product of slopes of line L and line K 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.


Let the line L be y=m1x+b1
and line K be y=m2x+b2

Statement 1 :
(-b1/m1)*(-b2/m2)>0 we don't know anything about b1 and b2. Hence insufficient.

Statement 2 :

b1.b2<0 here we have no information about the slopes m1 and m2 of two lines. Hence insufficient.

Statement 1+2

From 1 (-b1/m1)*(-b2/m2)>0
or (b1/m1)*(b2/m2)>0...(1)

From 2 we have b1.b2<0
So in order for (1)to stand true m1.m2 must be less than zero i.e negative.

Answer C

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Re: In the XY-coordinate plane, is the product of slopes [#permalink]
18 Oct 2021, 23:45
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