deepthit wrote:
this question can be simplified to |m - n|= |m| - |n| : are both m and n are positive ?
statement1 : not sufficient : no idea of signs of m and n
statement 2 : not sufficient : still can not determine signs of m and n
(1) + (2) together, NOt sufficient
Option E
Not exactly. E.g. if m = -3 & n = -2 then also the condition is fulfilled.
Hence the question can be transformed into: Do m & n have the same sign AND is |m | > | n |. If yes then condition holds good or else it fails.
Let's look at the question now:
Statement-1: m > n. Gives no idea about the sign of m & n. If m = 3 & n = 2 then the answer is Yes whereas if m = 3 & n = -2 then the answer is No. Insufficient.
Statement-2: m + 2n > 0 ---> m > -2n. Gives no idea about the sign of m & n. E.g. if n = 2 then m > -4. Now, m can be of same sign as n or can be of different sign. If m & n have the same sign AND if |m | > | n | then the answer is Yes (e.g. m = 3 & n = 2) whereas if m & n have the different sign (e.g. m = -3 & n = 2) or if |m | > | n | (e.g. m = 1 & n = 2) then the answer is No. Insufficient.
Combining both statements gives no new info.
m > n & m > -2n: say m = 5, n = 2. Then answer is Yes & if m = 5, n = -2 then the answer is No. Insufficient. Thus E is the answer.
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