Sorry ...the [spoiler]OA = C[/spoiler] and not A as stated above.
Also, its not the probability sum...its a line - slope sum.
Thanks
GMAT Prep : DS ( probability )
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limestone
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Equation for k and l line:
(l): y1 = a1* x1 + b1
(k): y2 = a2* x2 + b2
1. At x interception all y = 0, then
0 = a1*x1 + b1 => x1 = -b1/a1
0 = a2*x2 + b2 => x2 = -b2/a2
As x1*x2 >0 then b1*b2/a1*a2 >0
Can not determine whether a1*a2 >0 as be unable to define the sign of b1*b2 => insuff
2. At y interception all x = 0, then
y1 = b1
y2 = b2
As y1*y2 <0 then b1*b2 <0
This has nothing to do with a1*a2, then insuff.
1&2. We know:
b1*b2/a1*a2>0 and b1*b2 <0
Then a1*a2 <0 => suff.
Pick C.
(l): y1 = a1* x1 + b1
(k): y2 = a2* x2 + b2
1. At x interception all y = 0, then
0 = a1*x1 + b1 => x1 = -b1/a1
0 = a2*x2 + b2 => x2 = -b2/a2
As x1*x2 >0 then b1*b2/a1*a2 >0
Can not determine whether a1*a2 >0 as be unable to define the sign of b1*b2 => insuff
2. At y interception all x = 0, then
y1 = b1
y2 = b2
As y1*y2 <0 then b1*b2 <0
This has nothing to do with a1*a2, then insuff.
1&2. We know:
b1*b2/a1*a2>0 and b1*b2 <0
Then a1*a2 <0 => suff.
Pick C.
Last edited by limestone on Wed Oct 20, 2010 6:57 pm, edited 1 time in total.
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neerajkumar1_1
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the best is to visualize the figure...
but before i give u the soln...
there is one concept of line which should be clear to u..
slope is +ve for a line which we can see go upwards in the first quadrant
and slope is -ve for a line which we can see go downwards in the first quadrant
u can check this with values...
so here is the soln...
check the image below...
statement 1)
the product of x intercepts is positive...
that means they can either both be positive or negative...
so even thought we have the x intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .
statement 2)
the product of y intercepts is negative...
that means that one can +ve and one can be -ve...
again so even thought we have the y intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .
finally... together...
see the figure.. .
there is only 2 possibilities of drawing the lines... whose product of slopes will always give a -ve answer...
thus together the statements are sufficient...
Hope this helps...
but before i give u the soln...
there is one concept of line which should be clear to u..
slope is +ve for a line which we can see go upwards in the first quadrant
and slope is -ve for a line which we can see go downwards in the first quadrant
u can check this with values...
so here is the soln...
check the image below...
statement 1)
the product of x intercepts is positive...
that means they can either both be positive or negative...
so even thought we have the x intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .
statement 2)
the product of y intercepts is negative...
that means that one can +ve and one can be -ve...
again so even thought we have the y intercepts... we can draw the lines in any fashion... which will result in the product of their slopes being positive and negative.. .
finally... together...
see the figure.. .
there is only 2 possibilities of drawing the lines... whose product of slopes will always give a -ve answer...
thus together the statements are sufficient...
Hope this helps...
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GMATGuruNY
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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 line L and K is positive.
2) The product of the y-intercepts of line L and k is negative.
This is a visualization question. The trick is to see the different ways the lines could be drawn.
Statement 1: The x intercepts must either both be positive or both be negative.
Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) has an x intercept at (2,0). Slope is positive.
Positive * Positive = Positive
Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) and has an x intercept at (10,0). Slope is negative.
Positive * Negative = Negative.
Since the product can be both positive and negative, insufficient.
Statement 2: One y intercept must be positive, the other negative.
Line L passes through (4,3) and has a y intercept at (0,1). Slope is positive.
Line K passes through (4,3) and has a y intercept at (0,-1). Slope is positive.
Positive * Positive = Positive
Line L passes through (4,3) and has a y intercept at (0,10). Slope is negative.
Line K passes through (4,3) and has an y intercept at (0,-1). Slope is positive.
Negative * Positive = Negative.
Since the product can be both positive and negative, insufficient.
Statements 1 and 2 together:
For the product of the x intercepts to be positive, either both must be positive or both must be negative.
For the product of the y intercepts to be negative, one must be positive and the other must be negative.
If both x intercepts are negative, we won't be able to satisfy statement 2, because neither line will be able to pass through (4,3) and have a negative y intercept. Thus, both x intercepts must be positive.
So to satisfy both statements, we need 2 positive x intercepts, 1 positive y intercept, and 1 negative y intercept:
A positive x intercept and a positive y intercept will yield a negative slope.
A positive x intercept and a negative y intercept will yield a positive slope.
Negative * Positive = Negative.
Suffficient.
The correct answer is C.
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.
This is a visualization question. The trick is to see the different ways the lines could be drawn.
Statement 1: The x intercepts must either both be positive or both be negative.
Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) has an x intercept at (2,0). Slope is positive.
Positive * Positive = Positive
Line L passes through (4,3) and has an x intercept at (1,0). Slope is positive.
Line K passes through (4,3) and has an x intercept at (10,0). Slope is negative.
Positive * Negative = Negative.
Since the product can be both positive and negative, insufficient.
Statement 2: One y intercept must be positive, the other negative.
Line L passes through (4,3) and has a y intercept at (0,1). Slope is positive.
Line K passes through (4,3) and has a y intercept at (0,-1). Slope is positive.
Positive * Positive = Positive
Line L passes through (4,3) and has a y intercept at (0,10). Slope is negative.
Line K passes through (4,3) and has an y intercept at (0,-1). Slope is positive.
Negative * Positive = Negative.
Since the product can be both positive and negative, insufficient.
Statements 1 and 2 together:
For the product of the x intercepts to be positive, either both must be positive or both must be negative.
For the product of the y intercepts to be negative, one must be positive and the other must be negative.
If both x intercepts are negative, we won't be able to satisfy statement 2, because neither line will be able to pass through (4,3) and have a negative y intercept. Thus, both x intercepts must be positive.
So to satisfy both statements, we need 2 positive x intercepts, 1 positive y intercept, and 1 negative y intercept:
A positive x intercept and a positive y intercept will yield a negative slope.
A positive x intercept and a negative y intercept will yield a positive slope.
Negative * Positive = Negative.
Suffficient.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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