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12 Nov 2018, 00:24
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (02:00) correct
43%
(01:46)
wrong
based on 221
sessions
History
Date
Time
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Not Attempted Yet
In the XY-plane, the line l passes through the origin and the point (m, n), where mn ≠ 0. Is n > 0?
(1) The line l has a negative slope.
(2) m < n
(1) The line l has a negative slope.
(2) m < n
12 Nov 2018, 09:34
Kudos
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Since line passes through origin, line should be in the form of y = k*x where k is the slope.
This line passes through (m,n), so we get: n = k*m or k = n/m
Given mn is not equal to 0, hence, m or n is not zero.
Stmt 1: slope is negative. or k<0, which means (n/m) < 0
This can be possible when n is -ve and m is +ve or n is +ve and m is -ve. Since we can't determine signs of n and m definitely, this statement is insuff. Eliminate A, D
Stmt 2: m < n, we know k = n/m, but both m and n can be positive, both negative or n positive and m negative. So cannot be determined. Hence Insufficient. Eliminate B.
Combined: m < n and we know k has to be less than 0. This can be only possible when n is positive and m is negative. If m and n have the same sign, then k will be positive. Hence n>0. Hence sufficient.
Option C
This line passes through (m,n), so we get: n = k*m or k = n/m
Given mn is not equal to 0, hence, m or n is not zero.
Stmt 1: slope is negative. or k<0, which means (n/m) < 0
This can be possible when n is -ve and m is +ve or n is +ve and m is -ve. Since we can't determine signs of n and m definitely, this statement is insuff. Eliminate A, D
Stmt 2: m < n, we know k = n/m, but both m and n can be positive, both negative or n positive and m negative. So cannot be determined. Hence Insufficient. Eliminate B.
Combined: m < n and we know k has to be less than 0. This can be only possible when n is positive and m is negative. If m and n have the same sign, then k will be positive. Hence n>0. Hence sufficient.
Option C
08 Jun 2019, 07:43
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Bunuel
(1) The line l has a negative slope.
--> Line l passes through II and IV Quadrant
II Quadrant (m, n) = (-, +) --> m < n
IV Quadrant (m, n) = (+, -) --> m > n
So, Insufficient
(2) m < n
--> Many possibilities
(1, 2) --> n >0
(-2, -1) --> n <0
So, Insufficient
Combining (1) & (2)
Only possibility --> II Quadrant (m, n) = (-, +) --> m < n
Sufficient
So, Option C
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