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geet_ge: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Dec 23, 2011 8:09 pm

by geet_ge » Sat Feb 04, 2012 4:33 am

In the xy co ordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?

1)The product of x intercept of lines l and k is positive
2)The product of y intercept of lines l and k is negative

1)A Alone sufficient
2)B Alone sufficient
3)Together sufficient
4) Either
5) Neither

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Source: Beat The GMAT — Data Sufficiency | Sat Feb 04, 2012 4:33 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Feb 04, 2012 4:37 am

geet_ge wrote:In the xy co ordinate plane, line l and line k intersect at the point (4,3). Is the product of their slopes negative?

1)The product of x intercept of lines l and k is positive
2)The product of y intercept of lines l and k is negative

1)A Alone sufficient
2)B Alone sufficient
3)Together sufficient
4) Either
5) Neither

Let the equation of line L be y = m1x + c1.
Let the equation of line K be y = m2x + c2.
We need to know whether m1 * m2 is negative or not.

(1) x-intercept of L is -c1/m1.
x-intercept of K is -c2/m2.
So, (c1 * c2)/(m1 * m2) > 0.
But this does not tell us whether m1 * m2 < 0 or not; NOT sufficient.

(2) y-intercept of L is c1.
y-intercept of K is c2.
So, c1 * c2 < 0.
Again this does not tell us whether m1 * m2 < 0 or not; NOT sufficient.

Combining (1) and (2), (c1 * c2)/(m1 * m2) > 0 and c1 * c2 < 0.
This automatically means that m1 * m2 < 0.
So, both statements together are sufficient to answer the question.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
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mankey: Legendary Member; Posts: 627; Joined: Thu Jun 23, 2011 9:12 amFollowed by: 1 member; Thanked: 4 times

by mankey » Sat Feb 04, 2012 10:05 pm

Thanks Anurag. But what do you do with the information that the two lines intersect at (4,3)? How do you make out it is the extraneous information?

Thanks.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Feb 05, 2012 7:41 pm

mankey wrote:Thanks Anurag. But what do you do with the information that the two lines intersect at (4,3)? How do you make out it is the extraneous information?

Thanks.

We got the answer C, without using the info about the intersection point of the lines. So this is the extraneous information.

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pappueshwar: Master | Next Rank: 500 Posts; Posts: 234; Joined: Fri Oct 01, 2010 7:28 pmFollowed by: 4 members; Location: chennai; Thanked: 5 times

by pappueshwar » Tue Feb 14, 2012 9:40 am

hi Anurag,
ur expln is amazing for this problem,

i have a basic doubt

in any equation y = mx+b, b stands for y intercept.

now how to find the x intercept of this equation? from the problem it looks like u have taken -yintercept/ slope to find the x - intercept.
can u explain with an example ...

thanks

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