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

Question

(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

Salsanousi · Answer

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

GMATinsight · Answer

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) 
 https://gmatclub.com/forum/download/file.php?mode=view&id=44625

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) 
 https://gmatclub.com/forum/download/file.php?mode=view&id=44626 
X intercept in one case is +ve and in other case it's -ve hence
NOT SUFFICIENT

Answer: Option A

GMATinsight · Answer

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.

Salsanousi · Answer

GMATinsight  thanks!! I missed that out :/

Posted from my mobile device

BrentGMATPrepNow · Answer

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: 
 https://i.imgur.com/OR1Y6HZ.png 
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: 
 https://i.imgur.com/8mQ460i.png 
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 . 
 https://i.imgur.com/AFnhskw.png 
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 . 
 https://i.imgur.com/RvxmId4.png 
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

Cheers,
Brent

Rashed12 · Answer

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.

bumpbot · Answer

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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?

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