If m and n are integers, then what is the value of (-1)^m : GMAT Data Sufficiency (DS)
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If m and n are integers, then what is the value of (-1)^m

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

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New post 01 Mar 2011, 00:18
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
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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

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

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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

Chapter name: exponents and roots, page: 280, problem set k, number : 5

my solution:
[Reveal] Spoiler:
clearly we can see that m and n both are odd numbers, no matter how long they are , they are just odd numbers.
And there is no chance of m or n to be even because they are given pronouncedly……. So the answer must be (C), because together the statements are sufficient to answer the question.

But the book says, the answer is (B) . the author imagined the m and n sometimes odd and sometimes even to evaluate the answer…….!!!

Have you seen this ?

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Last edited by Bunuel on 15 May 2014, 03:10, edited 4 times in total.
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Re: If m and n are integers, then what is the value of (-1)^m [#permalink]

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New post 01 Aug 2013, 10:23
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Asifpirlo wrote:
Chapter name: exponents and roots, page: 280, problem set k, number : 5

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

my solution:
clearly we can see that m and n both are odd numbers, no matter how long they are , they are just odd numbers.
And there is no chance of m or n to be even because they are given pronouncedly……. So the answer must be (C), because together the statements are sufficient to answer the question.

But the book says, the answer is (B) . the author imagined the m and n sometimes odd and sometimes even to evaluate the answer…….!!!

Have you seen this ?


The answer will neither be C nor B. It is D

From F.S 1, we know that m = odd and \((-1)^{odd} = -1\).
Thus, \((-1)^m + (-1)^n + (-1)^m . (-1)^n = -1+(-1)^n-1*(-1)^n = -1\). We get a unique distinct numerical value, Sufficient.

Similarly,from F.S 2, we know that n = odd and thus,
\((-1)^m + (-1)^n + (-1)^m . (-1)^n = -1+(-1)^m-1*(-1)^m = -1\). We get a unique distinct numerical value, Sufficient.

D.
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Re: If m and n are integers, then what is the value of (-1)^m [#permalink]

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New post 01 Aug 2013, 14:16
mau5 wrote:
Asifpirlo wrote:
Chapter name: exponents and roots, page: 280, problem set k, number : 5

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

my solution:
clearly we can see that m and n both are odd numbers, no matter how long they are , they are just odd numbers.
And there is no chance of m or n to be even because they are given pronouncedly……. So the answer must be (C), because together the statements are sufficient to answer the question.

But the book says, the answer is (B) . the author imagined the m and n sometimes odd and sometimes even to evaluate the answer…….!!!

Have you seen this ?


The answer will neither be C nor B. It is D

From F.S 1, we know that m = odd and \((-1)^{odd} = -1\).
Thus, \((-1)^m + (-1)^n + (-1)^m . (-1)^n = -1+(-1)^n-1*(-1)^n = -1\). We get a unique distinct numerical value, Sufficient.

Similarly,from F.S 2, we know that n = odd and thus,
\((-1)^m + (-1)^n + (-1)^m . (-1)^n = -1+(-1)^m-1*(-1)^m = -1\). We get a unique distinct numerical value, Sufficient.

D.


good job man...yes it is an obvious (D)...thanks for sorting out........
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Re: If m and n are integers, then what is the value of (-1)^m [#permalink]

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New post 15 May 2014, 02:38
Sorry, dint understand.
How did you get -1 in both the cases.
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Re: If m and n are integers, then what is the value of (-1)^m [#permalink]

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seabhi wrote:
Sorry, dint understand.
How did you get -1 in both the cases.



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

Note that (-1)^ Odd power =-1 and (-1)^Even power =1 and (-1)^0 = 1

St 1 says m is odd so we have the expression as -1 +(-1)^n + (-1)*(-1)^n---------> Thus we get\(-1+(-1)^n - (-1)^n\) or -1

So St1 is sufficient

St 2 says n is odd so we have \((-1)^m + -1 *(-1)^m or -1\)
That's why Ans is D

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

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Re: If m and n are integers, then what is the value of ( 1)^m +   [#permalink] 09 Sep 2016, 04:39
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