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12 Sep 2019, 00:06
Kudos
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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:
52% (01:56) correct
48%
(01:50)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
for all integers m and n, m - n > 0. Is n > 0 ?
(1) \(m^2\) - \(n^2\) > 0
(2) mn > 0
(1) \(m^2\) - \(n^2\) > 0
(2) mn > 0
12 Sep 2019, 02:37
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for all integers m and n, m - n > 0. Is n > 0 ?
This tells us that m>n, but both m and n can positive or negative
(1) \(m^2\) - \(n^2\) > 0
\(m^2\) - \(n^2\) > 0.......\((m-n)(m+n)>0\)
We know m-n>0, so m+n>0
But nothing can be said about n..
If m is 4 and n=-2, 4-2>0
If m=4 and n=2, m+n>0 again
so n can be both positive or negative
Insuff
(2) mn > 0
This just tells us that both m and n are of same sign..
Both positive 4*2>0 OR both negative (-1)(-2)>0
Insuff
Combined..
We know m+n>0 and mn >0..
Thus m and n have SAME sign and m+n will be positive ONLY when atleast m is positive, so both m and n are POSITIVE..
Suff
C
This tells us that m>n, but both m and n can positive or negative
(1) \(m^2\) - \(n^2\) > 0
\(m^2\) - \(n^2\) > 0.......\((m-n)(m+n)>0\)
We know m-n>0, so m+n>0
But nothing can be said about n..
If m is 4 and n=-2, 4-2>0
If m=4 and n=2, m+n>0 again
so n can be both positive or negative
Insuff
(2) mn > 0
This just tells us that both m and n are of same sign..
Both positive 4*2>0 OR both negative (-1)(-2)>0
Insuff
Combined..
We know m+n>0 and mn >0..
Thus m and n have SAME sign and m+n will be positive ONLY when atleast m is positive, so both m and n are POSITIVE..
Suff
C
13 Nov 2023, 22:36
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