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

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
If m and n are integers, then what is the value of (–1)^m + (–1)^n +  [#permalink]

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04 Nov 2019, 03:22
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Difficulty:

75% (hard)

Question Stats:

37% (01:46) correct 63% (01:15) wrong based on 33 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) $$n = 63522251$$

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Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: If m and n are integers, then what is the value of (–1)^m + (–1)^n +  [#permalink]

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04 Nov 2019, 05:44
If m and n are integers, then what is the value of $$(–1)^m + (–1)^n + (–1)^m*(–1)^n$$ ?

(1) $$m = 23522101$$
so m is ODD....
(-1)^m=-1...$$(–1)^m + (–1)^n + (–1)^m*(–1)^n$$ =$$–1 + (–1)^n –1*(–1)^n$$
If n is odd...-1-1-1*-1=-2+1=-1
If n is even...-1+1-1*1=-1
So -1 always...Suff

(2) $$n = 63522251$$
so n is ODD....
(-1)^n=-1...$$(–1)^m + (–1)^n + (–1)^m*(–1)^n$$ =$$–1 + (–1)^m –1*(–1)^m$$
If m is odd...-1-1-1*-1=-2+1=-1
If m is even...-1+1-1*1=-1
So -1 always...Suff

D
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Re: If m and n are integers, then what is the value of (–1)^m + (–1)^n +   [#permalink] 04 Nov 2019, 05:44
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