(-3, 3) lie on line k?

[grandh01]

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

[Brent@GMATPrepNow]

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

[Brent@GMATPrepNow]

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]

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

[Brent@GMATPrepNow]

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]

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?

[Jim@StratusPrep]

It does not pass through it....

[Brent@GMATPrepNow]

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

[das.ashmita]

You are right Brent!
My bad. I dint notice the signs.

[Scott@TargetTestPrep]

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