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exponents of -1: experts pls help

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by mathewmithun » Fri May 25, 2012 3:29 am
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.
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by Anurag@Gurome » Fri May 25, 2012 3:39 am
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.

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Anurag Mairal, Ph.D., MBA
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Gurome, Inc.
1-800-566-4043 (USA)

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by ronnie1985 » Fri May 25, 2012 10:28 am
I agree that the answer is (D)
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by mathewmithun » Tue May 29, 2012 1:58 am
Anurag@Gurome wrote:
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?
Hi Anurag, the source of this question Nova's Data sufficiency Prep course.
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