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14 Feb 2012, 08:55
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C
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Difficulty:
55%
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Question Stats:
54% (01:22) correct
46%
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wrong
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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.
(1) The point (3;-3) does not lie on line k.
(2) The slope of line k is -1.
14 Feb 2012, 10:21
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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.
(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.
General Discussion
23 May 2020, 08:07
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rxs0005
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.
(1) The point (3;-3) does not lie on line k.
(2) The slope of line k is -1.
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
\(-3 + 3 \neq c; c \neq 0\)
For the point (-3; 3) to lie on line k; 3 -3 = 0 should be c
But \(c \neq 0\)
The point (-3,3) does not lie on line k
SUFFICIENT
IMO C
