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# Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15

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Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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31 Mar 2017, 07:22
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Difficulty:

55% (hard)

Question Stats:

44% (00:48) correct 56% (00:57) wrong based on 25 sessions

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Is $$(m+n)^3$$ an odd number?

1) m and n are integers
2) mn=15

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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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31 Mar 2017, 07:46
For statement 1 if m & n are both odd intergers then (m+n)3 will be even , but if m and n are one even other odd then (m+n)3 will odd so not sufficient

Statement 2 is insufficient as we don't know whether the numbers are integer or not and there can be many possibilities

On combining both statements
MN=15 so the factors will be 5×3
Or 15×1
In both cases we get (m+n)3 to be even hence combining they are sufficient

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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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31 Mar 2017, 07:56
B. a luck cuz I skipped the last deduction
st. 1 clearly insufficient
st. 2: nm = 15, if n,m = integer - (1;15), (3,5) and so on, => (n+m) even -> answered
if n, m not integer, let say 15/2 and 2 -> far from natural number to be odd (I tried to come up with a formula, but 've failed.)
anyone?
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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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04 Apr 2017, 16:14
Come on, B is wrong.

Try this:
1) m = 1, n = 15: (m+n) - even, and $$(m+n)^3$$ is also even;
2) m = 9/2+$$\sqrt{21}$$/2, n = 9/2-$$\sqrt{21}$$/2: (m+n) - odd, and $$(m+n)^3$$ is odd

C is the correct answer as both integer decompositions of 15 (3, 5 and 1, 15) give the even (m+n).
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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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04 Apr 2017, 23:21
wihi wrote:
Come on, B is wrong.

Try this:
1) m = 1, n = 15: (m+n) - even, and $$(m+n)^3$$ is also even;
2) m = 9/2+$$\sqrt{21}$$/2, n = 9/2-$$\sqrt{21}$$/2: (m+n) - odd, and $$(m+n)^3$$ is odd

C is the correct answer as both integer decompositions of 15 (3, 5 and 1, 15) give the even (m+n).

Selection of numbers in point 2 is awesome ....
The creator of this question missed that complex number selection :p
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GRE 1: Q167 V147
Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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08 Apr 2017, 02:34
ziyuen wrote:
Is $$(m+n)^3$$ an odd number?

1) m and n are integers
2) mn=15

Hi Bunuel,
I don't understand why (2) is SUFFICIENT.
if m = 15/4 n = 4,m+n is not integer.Hence,$$(m+n)^{3}$$ can't be considered odd number.
if m = 3 n = 5,$$(m+n)^{3}$$ is even.

Thanks
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Posts: 48061
Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15  [#permalink]

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08 Apr 2017, 04:01
sleepynut wrote:
ziyuen wrote:
Is $$(m+n)^3$$ an odd number?

1) m and n are integers
2) mn=15

Hi Bunuel,
I don't understand why (2) is SUFFICIENT.
if m = 15/4 n = 4,m+n is not integer.Hence,$$(m+n)^{3}$$ can't be considered odd number.
if m = 3 n = 5,$$(m+n)^{3}$$ is even.

Thanks

(2) is not sufficient. It's a poor quality question.

Topic is locked.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15 &nbs [#permalink] 08 Apr 2017, 04:01
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