mathewmithun wrote:If m and n are integers, then what is the value of (-1)^m+(-1)^n+(-1)^m.(-1)^n?
1. m=2342521
2. n=452341
OA is B but IMO it is D. Pls help.
(1) m = 2342521
(-1)^m + (-1)^n + (-1)^m.(-1)^n = (-1)^2342521 + (-1)^n + (-1)^(2342521).(-1)^n
= -1 + (-1)^n - (-1)^n
If n = odd, then (-1)^m + (-1)^n + (-1)^m.(-1)^n = -1 - 1 + 1 = -1
If n = even, then (-1)^m + (-1)^n + (-1)^m.(-1)^n = -1 + 1 - 1 = -1
In both the cases value of (-1)^m + (-1)^n + (-1)^m.(-1)^n = -1; SUFFICIENT.
(2) n = 452341
(-1)^m + (-1)^n + (-1)^m.(-1)^n = (-1)^m + (-1)^(452341) + (-1)^(452341).(-1)^m
= (-1)^m - 1 - (-1)^m
If m = odd, then (-1)^m + (-1)^n + (-1)^m.(-1)^n = -1 - 1 + 1 = -1
If m = even, then (-1)^m + (-1)^n + (-1)^m.(-1)^n = 1 - 1 - 1 = -1
In both the cases value of (-1)^m + (-1)^n + (-1)^m.(-1)^n = -1; SUFFICIENT.
The correct answer should be
D.
What's the source of this question?
