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BrentGMATPrepNow
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In the x-y coordinate plane, does line k have a positive x-intercept? 19 Oct 2018, 07:47
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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

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A
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In the x-y coordinate plane, does line k have a positive x-intercept? 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.
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GMATPrepNow
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
Show more

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.

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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 6638 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 6635 times ]

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In the x-y coordinate plane, does line k have a positive x-intercept? 19 Oct 2018, 09:04
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GMATPrepNow
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
Show more

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
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In the x-y coordinate plane, does line k have a positive x-intercept? 19 Oct 2018, 09:08
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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

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
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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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In the x-y coordinate plane, does line k have a positive x-intercept? 19 Oct 2018, 09:27
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GMATinsight thanks!! I missed that out :/

Posted from my mobile device
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In the x-y coordinate plane, does line k have a positive x-intercept? 21 Oct 2018, 16:02
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GMATPrepNow
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
Show more

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:

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:

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 .

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 .

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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In the x-y coordinate plane, does line k have a positive x-intercept? 11 Feb 2019, 01:28
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Salsanousi
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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

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.
Show more

I am not clear the below statement that you have mentioned above. Kindly help me how it happens.

If the slope is positive then the y-intercept is positive only way for this to be possible is when x-intercept is negative.
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In the x-y coordinate plane, does line k have a positive x-intercept? 10 Nov 2024, 08:00
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