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# If m and n are integers, then what is the value of ( 1)^m +

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Intern
Joined: 19 Sep 2010
Posts: 14
Followers: 0

Kudos [?]: 14 [0], given: 4

If m and n are integers, then what is the value of ( 1)^m + [#permalink]

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01 Mar 2011, 01:00
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25% (03:05) correct 75% (01:03) wrong based on 7 sessions

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If m and n are integers, then what is the value of (–1)^m + (–1)^n + (–1)^m · (–1)^n ?
(1) m = 23522101
(2) n = 63522251
Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

Kudos [?]: 38 [0], given: 0

Re: don't know how to crack [#permalink]

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01 Mar 2011, 01:18
Hi,
If you try to group the terms then you will see the solution.
[(-1)^m]*[(-1)^n+(1)]+[(-1)^n]

From A we know that m is odd so the sign will be neg. So no matter what the sign of n is the ans is -1.
from b we know that n is odd which means that the sign is neg. The term in the [] is 0, and the ans is -1.

Hope it helps
Manager
Joined: 14 Feb 2011
Posts: 196
Followers: 4

Kudos [?]: 101 [1] , given: 3

Re: don't know how to crack [#permalink]

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01 Mar 2011, 02:03
1
KUDOS
The given expression is $$(-1)^m+(-1)^n+(-1)^m.(-1)^n$$

From statement 1, m is odd so $$(-1)^m$$ = -1

Substituting this value in equation gives us $$-1 +(-1)^n - (-1)^n$$ = -1

So, sufficient

From statement 2, n is odd so $$(-1)^n$$ = -1

Substituting this value in equation gives us $$-1 +(-1)^m - (-1)^m$$ = -1

So, sufficient

Manager
Status: I am Midnight's Child !
Joined: 04 Dec 2009
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WE 1: Software Design and Development
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Kudos [?]: 55 [0], given: 11

Re: don't know how to crack [#permalink]

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01 Mar 2011, 09:43
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Joined: 14 Dec 2010
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Concentration: Technology, Entrepreneurship
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Kudos [?]: 30 [0], given: 5

Re: don't know how to crack [#permalink]

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02 Mar 2011, 00:29
I feel substituting is faster than grouping.D it is.
Re: don't know how to crack   [#permalink] 02 Mar 2011, 00:29
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