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08 Jun 2020, 11:23
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
48% (02:07) correct
52%
(02:14)
wrong
based on 111
sessions
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In the xy- plane, lines l and k intersect at point A whose x and y coordinates are positive. If the lines l and k are not parallel to either of the axes, is the product of the slopes of line l and k greater than zero?
(1) The product of the x-intercepts of the lines l and k is negative.
(2) The product of the y-intercepts of the lines l and k is positive.
Are You Up For the Challenge: 700 Level Questions
(1) The product of the x-intercepts of the lines l and k is negative.
(2) The product of the y-intercepts of the lines l and k is positive.
Are You Up For the Challenge: 700 Level Questions
08 Jun 2020, 12:09
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IMO :- C
Line intercept formula
x/a + y/b =1
lets x-intercept be a1, a2 and y-intercept be b1, b2
Slope = (-) b/a
Product of slope = (+) (b1*b2) / (a1 *a2)
Option 1 :- a1*a2<0 ,not sufficient
Option 2 :- b1*b2 >0, not suffcient
But Combining both we have -ve Product
Suffcient
Line intercept formula
x/a + y/b =1
lets x-intercept be a1, a2 and y-intercept be b1, b2
Slope = (-) b/a
Product of slope = (+) (b1*b2) / (a1 *a2)
Option 1 :- a1*a2<0 ,not sufficient
Option 2 :- b1*b2 >0, not suffcient
But Combining both we have -ve Product
Suffcient
General Discussion
09 Jun 2020, 09:05
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This is almost identical to the official GMATPrep problem here:
https://gmatclub.com/forum/in-the-xy-co ... 93771.html
The best way to answer questions like this is to draw diagrams to see what possibilities there are. Here, we know our lines meet at some point in the first quadrant. We want to know if the two lines are either both rising or both falling (then their slopes would have the same sign, and so would give us a positive product).
If Statement 1 is true, one x-intercept is left of the origin, one is right of the origin. If a line has a negative x-intercept, and then rises to some point in the first quadrant, it must have a positive slope. But for the other line, we can't be sure - the slope can be positive or negative depending where the x-intercept is.
If Statement 2 is true, both y-intercepts are either above the origin or below the origin. If both are below, then both slopes are positive. But if both are above the origin, we can't be sure if we have negative or positive slopes.
Using both Statements, from Statement 1, as explained, we know one line has a negative x-intercept and a positive slope. So it must have a positive y-intercept. From Statement 2, the second line must have a positive y-intercept too, and a positive x-intercept from Statement 1. That line must be falling as it moves right, so must have a negative slope. So using both Statements, we can be sure we have slopes of opposite signs, and the answer is C.
Obviously a lot faster just to draw the diagrams than to write up the solution in words.
https://gmatclub.com/forum/in-the-xy-co ... 93771.html
The best way to answer questions like this is to draw diagrams to see what possibilities there are. Here, we know our lines meet at some point in the first quadrant. We want to know if the two lines are either both rising or both falling (then their slopes would have the same sign, and so would give us a positive product).
If Statement 1 is true, one x-intercept is left of the origin, one is right of the origin. If a line has a negative x-intercept, and then rises to some point in the first quadrant, it must have a positive slope. But for the other line, we can't be sure - the slope can be positive or negative depending where the x-intercept is.
If Statement 2 is true, both y-intercepts are either above the origin or below the origin. If both are below, then both slopes are positive. But if both are above the origin, we can't be sure if we have negative or positive slopes.
Using both Statements, from Statement 1, as explained, we know one line has a negative x-intercept and a positive slope. So it must have a positive y-intercept. From Statement 2, the second line must have a positive y-intercept too, and a positive x-intercept from Statement 1. That line must be falling as it moves right, so must have a negative slope. So using both Statements, we can be sure we have slopes of opposite signs, and the answer is C.
Obviously a lot faster just to draw the diagrams than to write up the solution in words.
