by: DeepGOO225
18 mins
by: DeepGOO225
19 mins
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Difficulty:
25%
(medium)
Question Stats:
64% (00:49) correct
36%
(00:57)
wrong
based on 73
sessions
History
Date
Time
Result
Not Attempted Yet
Is mn < 0?
(1) \(m^5n^2 < 0\)
(2) \(m^{11}p^8n^5 < 0\)
_________________
(1) \(m^5n^2 < 0\)
(2) \(m^{11}p^8n^5 < 0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Bunuel
WE require to find whether m and n are of opposite sign..
lets see the statements
(1) \(m^5n^2 < 0\)...
\(m*m^4*n^2 < 0\)..
\(m^4n^2 > 0\) so m<0
but we do not know anything about n
if n>0.. YES
if n<0.. NO
Insuff
(2) \(m^{11}p^8n^5 < 0\)
\(m*m^{10}*p^8*n*n^4 < 0\)..
\(m*n*m^{10}*p^8*n^4 < 0\)..
Now \(m^{10}*p^8*n^4 > 0\).. so mn<0
ans is YES
Suff
B
_________________
Is mn < 0?
(1) \(m^5n^2 < 0\)
(2) \(m^{11}p^8n^5 < 0\)
Is mn<0?
Statement 1: \(m^5n^2 < 0\)
n^2 is always +ve. So statement one only tells us that m is -ve. Now if n is positive, then we have a yes answer to the question in the prompt. However, if n is -ve the answer to the question in the prompt is No. Hence insufficient.
Statement 2: \(m^{11}p^8n^5 < 0\)
We know that p^8 is positive and m^11 x n^5 is -ve. So we know m and n have different signs. Therefor mn is always -ve.
Hence Statement 2 is sufficient. (Odd powers retain the signs of the original numbers)
B.
(1) \(m^5n^2 < 0\)
(2) \(m^{11}p^8n^5 < 0\)
Is mn<0?
Statement 1: \(m^5n^2 < 0\)
n^2 is always +ve. So statement one only tells us that m is -ve. Now if n is positive, then we have a yes answer to the question in the prompt. However, if n is -ve the answer to the question in the prompt is No. Hence insufficient.
Statement 2: \(m^{11}p^8n^5 < 0\)
We know that p^8 is positive and m^11 x n^5 is -ve. So we know m and n have different signs. Therefor mn is always -ve.
Hence Statement 2 is sufficient. (Odd powers retain the signs of the original numbers)
B.
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