push12345 wrote:

IS m >n

1)m^2 + n^2 >2mn

2) |m|n =m|n|

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(1) m^2 + n^2 > 2mn means that m^2 + n^2 - 2mn > 0

Or (m-n)^2 > 0. This will be true whenever m and n are unequal. So all this tells is that 'm' is not equal to 'n'. Not sufficient.

(2) |m|n =m|n|

This will be true either when both m/n are positive OR when both m/n are negative. So all this tells is that 'm' and 'n' have same sign. Not sufficient.

Combining the two statements, m and n have same signs and they are not equal. But still we cant say whether m > n or not.

Eg, m=3, n=2 satisfies both the statements. And m=2, n=3 also satisfies both the statements. Not sufficient.

Hence

E answer(OA is B. Please check if theres some error)