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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 + [#permalink]

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01 Mar 2011, 01:00
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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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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

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

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01 Mar 2011, 02:03
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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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01 Aug 2013, 09:20
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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, 04:10, edited 4 times in total.
Topic Renamed.Edited OA

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

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01 Aug 2013, 11:23
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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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01 Aug 2013, 15:16
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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15 May 2014, 03:38
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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15 May 2014, 04:01
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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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09 Sep 2016, 05:39
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Re: If m and n are integers, then what is the value of ( 1)^m +   [#permalink] 09 Sep 2016, 05:39
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# If m and n are integers, then what is the value of (-1)^m

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