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19 Oct 2018, 07:47
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A
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Difficulty:
55%
(hard)
Question Stats:
62% (01:46) correct
38%
(02:04)
wrong
based on 282
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In the x-y coordinate plane, does line k have a positive x-intercept?
(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0
*kudos for all correct solutions
(1) (slope of line k)(y-intercept of line k) > 0
(2) (slope of line k) - (y-intercept of line k) < 0
*kudos for all correct solutions
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Updated on: 19 Oct 2018, 09:39
Originally posted by Salsanousi on 19 Oct 2018, 08:17.
Last edited by Salsanousi on 19 Oct 2018, 09:39, edited 2 times in total.
Last edited by Salsanousi on 19 Oct 2018, 09:39, edited 2 times in total.
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If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.
The same is true for the slope is negative and y-intercept is negative
The x-intercept is negative.
Sufficient.
For statement 2)
If slope is positive then y intercept must be a larger positive for the statement to hold true and be negative.
If both are positive then x-intercept is negative.
Now if slope is negative then y-intercept is a smaller negative or a positive number.
X-intercept then can be positivbe or negative
Insufficient.
The answer is best understood by a drawing.
Answer choice A.
Thanks to GMATinsight for pointing out a mistake in my solution, I originally choose D.
Posted from my mobile device
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File comment: For statement 2
Screen Shot 2018-10-19 at 7.37.39 PM.png [ 31.78 KiB | Viewed 6595 times ]
File comment: For statement 1
Screen Shot 2018-10-19 at 7.37.33 PM.png [ 24.96 KiB | Viewed 6592 times ]
19 Oct 2018, 09:04
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Question: does line k have a positive x-intercept?
Statement 1: (slope of line k)(y-intercept of line k) > 0
Case 1: Both slope and y-intercept are +ve (Red Line)
Case 2: Both slope and y-intercept are -ve (Blue Line)
As per both cases, x-intercept is -ve hence
SUFFICIENT
Statement 2: (slope of line k) - (y-intercept of line k) < 0
i.e. (slope of line k) < (y-intercept of line k)
Case 1: Y-intercept = 3 and slope = 1 (Red Line)
Case 2: Y-intercept = 3 and slope = -1 (Blue Line)
X intercept in one case is +ve and in other case it's -ve hence
NOT SUFFICIENT
Answer: Option A
