grandh01 wrote:In the xy-plane, does the point (-3, 3) lie on line k?
(1) The point (3,-3) does not lie on line k.
(2) The slope of line k is -1.

OA IS C

Reworded target question: Does line k pass through the point (-3, 3)?

Statement 1: The point (3,-3) does not lie on line k.
It's still possible that line k passes through (-3, 3), and it's possible that line k does not pass through (-3, 3)
INSUFFICIENT

Statement 2: The slope of line k is -1.
It's still possible that line k passes through (-3, 3), and it's possible that line k does not pass through (-3, 3)
INSUFFICIENT

Statement 1 & 2:
When we combine the statements, we're told that a line with slope -1 does not pass through (3, -3)
Important: the slope between (-3, 3) and (3, -3) is -1. In other words, if line k were to have a slope of -1 and pass through (3, -3), then line k would definitely pass through (-3, 3)
Conversely, since the combined statements tell us that line k (with slope -1) does not pass through (3, -3), we can be certain that it definitely does not pass through (-3, 3)
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT and the answer is C.

Cheers,
Brent

For additional practice, here's another Data Sufficiency question that addresses the issue of whether or not a point is on a particular line:

https://www.beatthegmat.com/gmat-prep-pr ... 34740.html

Cheers,
Brent

jrakhe wrote:It seems that correct answer should be D.
1) Sufficient
2) Sufficient: As for line with -ve slope both x and y should have the same sign. But (-3, 3) have different signs so it will not lie on the line K. Sufficient.

Ans: D

Why do you feel that statement 1 is sufficient? All we know is that this line k does not include the point (3, -3). This tells us nothing about whether or not line k includes the point (-3, 3)

Regarding your position on statement 2, the negative slope does not imply that the coordinates must have different signs. For example, the line y = -1x + 2 has a slope of -1, but the point (1, 1) lies on this line. Here, both coordinates are positive.

The correct answer is C.

I hope this helps.

Cheers,
Brent

das.ashmita wrote:

Statement 1: The point (3,-3) does not lie on line k.
It's still possible that line k passes through (-3, 3), and it's possible that line k does not pass through (-3, 3)

Hi Brent
Can u please explain this. I am confused here. If point (3,-3) does not lie on line k, then how can the line k pass through it?

I think the confusion here is that (3, -3) and (-3, 3) look like the same point. Notice the placement of the negative sign.

Cheers,
Brent

grandh01 wrote: ↑

Tue Sep 25, 2012 9:17 pm

In the xy-plane, does the point (-3, 3) lie on line k?
(1) The point (3,-3) does not lie on line k.
(2) The slope of line k is -1.

OA IS C

Solution:

Statement One Alone:

The point (3, -3) does not lie on line k.

Even though we know (3, -3) does not lie on line k, we can’t determine whether (-3, 3) lies on the line or not. Statement one alone is not sufficient.

Statement Two Alone:

The slope of line k is -1.

Even though we know the slope of line k is -1, we can’t determine whether (-3, 3) lies on the line or not. There are many lines with a slope of -1 that do not pass through the point (-3, 3). Statement two alone is not sufficient.


Statements One and Two Together:

If (-3, 3) does lie on the line k with slope of -1, then (3, -3) will also lie on the line (notice that the slope of the line containing both points is (3 - (-3))/(-3 - 3)) = 6/(-6) = -1). However, since we know that (3, -3) does not lie on the line, then (-3, 3) can’t lie on the line, either. Both statements together are sufficient to answer the question.

Answer: C