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In the xy-coordinate plane, line l and line k intersect at

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In the xy-coordinate plane, line l and line k intersect at [#permalink] New post 18 Feb 2008, 18:01
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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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-xy-coordinate-plane-line-l-and-line-k-intersect-at-93771.html
[Reveal] Spoiler: OA
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 19 Feb 2008, 22:15
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To make using this editor easy, I am naming lines as 1 and 2
and thier x and y intercepts as x1, x2, y1 and y2

slope of line 1 = -y1/x1
slope of line 2 = -y2/x2

product of slopes = (y1*y2)/(x1*x2)
since numerator is -ve and denominator is +ve, product of slopes is -ve

What is OA?
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 20 Feb 2008, 10:53
Ohhhhhhhhhhhhhhh!!!!!!!!!! Thanks sreehari! I remember I got raped by this question on GMATPrep, I was trying to draw lines out over and over, lol! :-) That's so simple.

So line 1's slope is -y1/x1 & line 2's slope is -y2/x1

So the product of their slopes is y1*y2 / (x1*x2)

And if you take the stuff together, ah!!!!!!! Nice :-)
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 05 Jun 2011, 10:02
I still dont get it. Can someone please further explain in a more simple way?
Many thanks.
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 05 Jun 2011, 23:06
its ok now, i just got confused by the -y1 and -y2. thought its a negative sign.

Thanks
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 07 Jun 2011, 10:14
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bsjames2 wrote:
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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


Please explain your answer


This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 10 Jun 2011, 18:35
I answered correctly but after drawing lines all over....thanks Karishma for the explanation
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 26 Aug 2013, 01:44
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VeritasPrepKarishma wrote:
bsjames2 wrote:
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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


Please explain your answer


This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x





Thanks I realized it only now; slope =-(y intercept)/(x intercept)
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Re: In the xy-coordinate plane, line l and line k intersect at [#permalink] New post 26 Aug 2013, 01:58
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 18 May 2014, 06:06
VeritasPrepKarishma wrote:
bsjames2 wrote:
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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


Please explain your answer


This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x



Hi karishma

Slope of line 1 is -y1/x1
slope of line 2 is -y2/x2

if we multiply both the slopes
wont the product be positive??

Kindly help
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 18 May 2014, 07:15
adityagogia9899 wrote:
VeritasPrepKarishma wrote:
bsjames2 wrote:
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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


Please explain your answer


This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x



Hi karishma

Slope of line 1 is -y1/x1
slope of line 2 is -y2/x2

if we multiply both the slopes
wont the product be positive??

Kindly help


Hi Aditya,

y1 and x1 are the intercepts on y-axis and x-axis respectively by line 1 (or l) ; And we still don't know the intercepts are on negative or positive.
So it's possible that y1<0 or y1 >0 and similarly , x1<0 or x>0.
Similar cases hold true for y2 and x2.

So the value of the product (y1*y2)/(x1*x2) is required which would depend on the values of x1,y1,x2,y2

The two statements together can answer the value of the product (as negative )

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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 18 May 2014, 20:24
Expert's post
adityagogia9899 wrote:
Hi karishma

Slope of line 1 is -y1/x1
slope of line 2 is -y2/x2

if we multiply both the slopes
wont the product be positive??

Kindly help


Remember that y1, x1, y2 and x2 are all variables. They could be positive or negative.

Product of slopes = (y1/x1)*(y2/x2) = (y1*y2)/(x1*x2)
The product depends on whether y1, x1, x2, y2 are positive or negative. The statements tell you that x1*x2 is positive and y1*y2 is negative. So product of slopes = negative/positive which is negative.
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Re: GMAT Prep: XY-Coordinate Plane Ques [#permalink] New post 18 May 2014, 23:34
adityagogia9899 wrote:
VeritasPrepKarishma wrote:
bsjames2 wrote:
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 lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.


Please explain your answer


This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)

Above, sreehari uses this concept to solve the question very efficiently.

If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)

So slope = (y - 0)/(0 - x) = -y/x



Hi karishma

Slope of line 1 is -y1/x1
slope of line 2 is -y2/x2

if we multiply both the slopes
wont the product be positive??

Kindly help




The best approach to tackle statement questions in DS is as follows:

Step 1: Convert all the alphabetical statements in algebraic statements
Step 2: Reduce the number of variable to minimum
Step 3: Check how many variables are left. You may probably need that many statements to solve the questions but you might need lesser number of statements to answer the question.

Caution: Don't waste your time in solving the question. You have to analyse the data sufficiency and not solve the question.

Step 1: Introduce as many variable as required. In this case we require 4 variables: x1, y1, x2, y2
Reducing the alphabetical statement to algebraic one:

Product of slopes will be: (-y2/x2)*(-y1/x1) = y2y1/x2x1
We have to see if y2y1/x2x1<0?

Step 2: Reduce number of variables. In this case, we took 4 variables. But to determine the sign of slope we need to find out only two variable i.e. y2y1 and x2x1 and that two their signs and not their values. Thus, to answer the constraint we need to know 2 things and not 4.

Step 3: Check statements:

1) The product of the x-intercepts of lines l and k is positive.

This gives us the sign of x2x1 as positive. But we don't know whether y2y1 is positive or negative. Thus, this is not sufficient.

2) The product of the y-intercepts of lines l and k is negative.

This gives us the sign of y2y1 as positive. But we don't know whether x2x1 is positive or negative. Thus, this is not sufficient.

Now combining both these statements, we can know the sign of y2y1 as well as x2x1 which is coming out to be negative.

Thus, C becomes our solution.


Hope it is useful to you!!!

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Re: GMAT Prep: XY-Coordinate Plane Ques   [#permalink] 18 May 2014, 23:34
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