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In the x-y coordinate plane, does line k have a positive x-intercept?

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In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post 19 Oct 2018, 06:47
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Question Stats:

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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

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In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post Updated on: 19 Oct 2018, 08:39
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GMATPrepNow wrote:
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


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
Attachments

File comment: For statement 2
Screen Shot 2018-10-19 at 7.37.39 PM.png
Screen Shot 2018-10-19 at 7.37.39 PM.png [ 31.78 KiB | Viewed 298 times ]

File comment: For statement 1
Screen Shot 2018-10-19 at 7.37.33 PM.png
Screen Shot 2018-10-19 at 7.37.33 PM.png [ 24.96 KiB | Viewed 298 times ]


Originally posted by Salsanousi on 19 Oct 2018, 07:17.
Last edited by Salsanousi on 19 Oct 2018, 08:39, edited 2 times in total.
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Re: In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post 19 Oct 2018, 08:04
GMATPrepNow wrote:
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


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)
Image

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)
Image
X intercept in one case is +ve and in other case it's -ve hence
NOT SUFFICIENT

Answer: Option A
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Re: In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post 19 Oct 2018, 08:08
Salsanousi wrote:
GMATPrepNow wrote:
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


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 must be a smaller negative.


X-intercept is negative.

Sufficient.

The answer is best understood by a drawing.

Answer choice D.

Posted from my mobile device


I find some mistake in highlighted part Salsanousi

When slope is -1, Y-intercept may be +3 as well and (slope of line k) - (y-intercept of line k) = (-1) - (+3) < 0 also stays satisfied.
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Re: In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post 19 Oct 2018, 08:27
GMATinsight thanks!! I missed that out :/

Posted from my mobile device
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Re: In the x-y coordinate plane, does line k have a positive x-intercept?  [#permalink]

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New post 21 Oct 2018, 15:02
Top Contributor
GMATPrepNow wrote:
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


Target question: Does line k have a positive x-intercept?

Statement 1: (slope of line k)(y-intercept of line k) > 0
There are two possible cases that that satisfy statement 1:
- the slope and y-intercept are both positive
- the slope and y-intercept are both negative
Let's examine each case:

Case a: the slope and y-intercept are both positive
No matter now you sketch a line that has these two features, it will look something like this:
Image
As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: the slope and y-intercept are both negative.
No matter now you sketch a line that has these two features, it will look something like this:
Image
As you can see, the answer to the target question is NO, line k does NOT have a positive x-intercept

In both cases, the answer to the target question is the SAME.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (slope of line k) - (y-intercept of line k) < 0
There are several lines that satisfy statement 2. Here are two:
Case a:The line has a slope of -2 and y-intercept of -1 .
Image
In this case, the answer to the target question is NO, line k does NOT have a positive x-intercept

Case b: The line has a slope of -2 and y-intercept of 1 .
Image
In this case, the answer to the target question is YES, line k DOES have a positive x-intercept

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Brent
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Re: In the x-y coordinate plane, does line k have a positive x-intercept? &nbs [#permalink] 21 Oct 2018, 15:02
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