Is m ≠ n ? (1) (m – n)(m + n) m + n

Question

Is m ≠ n ?
 
(1) (m – n)(m + n) < 0 
(2) |m + n| > m + n

KrishnakumarKA1 · Answer

St 1: -n<m<n. therefore m is not equal to n ever. ANSWER

St 2: |m+n|<m+n. therefore m is not equal to n ever. ANSWER

option D

brunogr · Answer

ByjusGMATapp,

How can you conclude that m is not equal to n, if St 2 is just an impossible expression?

Mo2men · Answer

Dear Bunuel,

Is statement 2 correct? I tried to came up with any numbers to support but I failed.

I doubt that the question has something wrong.

Bunuel · Answer

Edited. It's |m + n|  >  m + n. Thank you.

Mo2men · Answer

Is m ≠ n ? 
 
 (1) (m – n)(m + n) < 0

If m=n or m=-n...........(m – n)(m + n) =0........this is not the case in fact 1

Therefore, m ≠ n

Sufficient

(2) |m + n| > m + n

Let m=n=-1 ..... |-1 - 1| > -1 - 1.........|-2| > -2........2>2...........Answer is NO

Let m -2 & n=1 ..... |-2 + 1| > -2 + 1.........|-1| > -1........1>-1...........Answer is Yes

Insufficient

Answer: A

chetan2u · Answer

(1) (m – n)(m + n) < 0 
 If m=n, then m-n=0, and (m – n)(m + n) will be 0. 
Thus, m ≠ n
Sufficient.

(2) |m + n| > m + n
Cases
(i)  m=n=negative number ........ |-2-2|>-2-2.....4>-4 .....answer is yes
(ii)  m and n are negative numbers but not equal ...... |-3-2|>-3-2......5>-5 ....answer is no

A

Is m ≠ n ? (1) (m – n)(m + n) < 0 (2) |m + n| > m + n

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