In the xy-plane, does the point (-3; 3) lie on line k?

Question

(1) The point (3;-3) does not lie on line k.
(2) The slope of line k is -1.

Bunuel · Accepted Answer

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.

Each statement alone is clearly insufficient.

When taken together: some line n, which passes through the two points (-3, 3) and (3, -3) has the slope equal to  m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-3}{3-(-3)}=-1 . Now, the slope of k is also -1 and since from (1) the point (3;-3) does not lie on line k, then k is parallel to n, thus the lines n and k, have no point in common, which means that the point (-3; 3), which is on n, does not lie on line k. Sufficient.

Answer: C.

Hope it's clear.

Kinshook · Answer

Asked: In the xy-plane, does the point (-3; 3) lie on line k?

(1) The point (3;-3) does not lie on line k.
Since there is no other information about line k
NOT SUFFICIENT

(2) The slope of line k is -1.
Equation of line k : y +x = c
Since c is unknown, line k is not defined.
NOT SUFFICIENT

(1) + (2) 
(1) The point (3;-3) does not lie on line k.
(2) The slope of line k is -1.
Equation of line k : y +x = c
Since (3,-3) does not lie on line k
 -3 + 3 
eq c; c 
eq 0 
For the point (-3; 3) to lie on line k; 3 -3 = 0 should be c
But  c 
eq 0 
The point (-3,3) does not lie on line k
SUFFICIENT

IMO C

ScottTargetTestPrep · Answer

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

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In the xy-plane, does the point (-3; 3) lie on line k?

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