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# In the xy-coordinate plane, line L and line K intersect at

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Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK
In the xy-coordinate plane, line L and line K intersect at [#permalink]

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29 Nov 2006, 10:55
1
KUDOS
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the xy-coordinate plane, line L and line K intersect at point (4,3). Is the product of their slopes negative?

(1) The product of the x-intercepts of lines L and K is positive

(2) The product of the y-intercepts of lines L and K is positive

How did you guys go about solving this?

For me...

??? (slope of L)*(slope of K) = negative number ???

--> the question is asking whether exactly one of the slopes is negative

(1) INSUFF both x intercepts could be positive or both negative
(2) INSUFF either y intercept of L is negative and for K positive or vice versa

I don't understand why together the statements are sufficient. Together, i come up with four possible scenarios but still not definite that one slope is negative.
_________________

Impossible is nothing

Manager
Joined: 03 Jul 2005
Posts: 192
Location: City

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29 Nov 2006, 11:10
I think it's because you can take A an assume that X coordinates are either both positive or both negative

From B you can assume that the Y coordinates are either both postive or both negative.

So taking both together you can assume that the slope will be positive?

Is the OA - C?
Manager
Joined: 04 Nov 2006
Posts: 158

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29 Nov 2006, 12:28
1
KUDOS
I also get C...here's the logic.

When you take the information given in (1) and (2) together, you can surmise that there are 4 possibilities for these two lines, K and L.

1st possibility -> both x intercepts are +ve and both y intercepts are -ve
In this case, both lines have to have +ve slope, and so the product of their slopes is positive.

2nd possibility -> both x intercepts are +ve and both y intercepts are +ve
In this case, both lines have to have -ve slope, and so the product of their slopes is positive.

3rd possibility -> both x intercepts are -ve and both y intercepts are -ve
In this case, both lines have to have -ve slope, and so the product of their slopes is positive.

4th possibility -> both x intercepts are -ve and both y intercepts are +ve
In this case, both lines have to have +ve slope, and so the product of their slopes is positive.

So, we know for sure that the product of the slopes is positive. i.e., we have sufficient information to answer this question.

Very good problem...
Senior Manager
Joined: 08 Jun 2006
Posts: 335
Location: Washington DC

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29 Nov 2006, 12:54
good one ..I am getting C too...
Senior Manager
Joined: 01 Oct 2006
Posts: 495

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29 Nov 2006, 13:53
Consider 2 eaquations
y1 =m1x1+c1
y2=m2x2+c2

Product of x intecepts = c1*c2/(m1*m2)
Product of y intercepts = c1*c2

St1 says c1*c2/(m1*m2) is +ve now m1*m2 can +ve or -ve so insuff
st2 says c1*c2 is +ve ....insuff

Combining 1 and 2 if c1*c2 is +ve and c1*c2/(m1*m2) is +ve then m1*m2 must be +ve

Thus C is suff to answer and hence its the correct choice
Senior Manager
Joined: 23 May 2005
Posts: 266
Location: Sing/ HK

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30 Nov 2006, 08:36
OA is C
_________________

Impossible is nothing

Intern
Joined: 18 Dec 2006
Posts: 5

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08 Jan 2007, 11:56
y=mx + c
Get two eqns using given conditions.
c1c2/m1m2>0
Use 1 and 2 gives m1m2 always +ve.

hence C.
Intern
Joined: 21 Nov 2006
Posts: 44

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09 Jan 2007, 09:27
Of the 4 scenarios is scenario 3 possible? With point 4,3 I think you can eliminate 3. Not that it matters as it is irrelevant to the answer.

Eric
Manager
Joined: 20 Dec 2004
Posts: 177

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09 Jan 2007, 17:24
Good explanation Yogesh. I like your approach.
_________________

Regards

Subhen

Senior Manager
Joined: 24 Nov 2006
Posts: 349
Re: GMAT Prep: XY plane [#permalink]

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09 Jan 2007, 21:17
(1) If the products of both x-intercepts are -ve: L could have +ve slope and K -ve slope, or both +ve, or both -ve. In the 1st case, the products of the slopes are negative, while in the 2nd and 3rd they are positive. Insuff => B, C or E.

(2) Similar to (1). Insuff => C or E.

(1&2) The only possible case is that both L and K are -ve-sloped lines => the product of their slopes has to be -ve and the question has one answer => C.
VP
Joined: 22 Oct 2006
Posts: 1438
Schools: Chicago Booth '11

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10 Jan 2007, 15:15
how do you get

c1*c2/(m1*m2) ?

Why is that the product of the X intercepts?
Senior Manager
Joined: 29 Jan 2007
Posts: 441
Location: Earth

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26 Feb 2007, 19:43
terp26

in equation y=m*x+c
u find out Y intercept by putting X =0 and you get Y intercept is C
so same way you put y = 0 to get X intercept which will be -c/m

So if you have 2 lines.
product will be
(-c1/m1)*(-c2/m2) => c1c2/m1m2

Yogesh good thinking there.

I believe in this question... information that lines intersect at (4,3) is redundant.

another point I will add is... you will notice that

product of slopes = product of Y intercepts / product of X intercepts.

so when condition 1) and 2) are both given then product of slopes has to be positive.
Manager
Joined: 22 Sep 2009
Posts: 215
Location: Tokyo, Japan

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23 Nov 2009, 20:07
yogeshsheth wrote:
Consider 2 eaquations
y1 =m1x1+c1
y2=m2x2+c2

Product of x intecepts = c1*c2/(m1*m2)
Product of y intercepts = c1*c2

St1 says c1*c2/(m1*m2) is +ve now m1*m2 can +ve or -ve so insuff
st2 says c1*c2 is +ve ....insuff

Combining 1 and 2 if c1*c2 is +ve and c1*c2/(m1*m2) is +ve then m1*m2 must be +ve

Thus C is suff to answer and hence its the correct choice

Great thinking here. I just use the 4 scenarios and draw it out. It is so much faster with this test
Re:   [#permalink] 23 Nov 2009, 20:07
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