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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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New post 31 Mar 2017, 06:22
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Is \((m+n)^3\) an odd number?

1) m and n are integers
2) mn=15
[Reveal] Spoiler: OA

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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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New post 31 Mar 2017, 06:46
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
Answer c

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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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New post 31 Mar 2017, 06:56
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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New post 04 Apr 2017, 15:14
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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New post 04 Apr 2017, 22:21
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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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15 [#permalink]

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New post 08 Apr 2017, 01:34
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.

Please help clarify
Thanks
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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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New post 08 Apr 2017, 03:01
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.

Please help clarify
Thanks


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

Topic is locked.
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Re: Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15   [#permalink] 08 Apr 2017, 03:01
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Is (m+n)3 an odd number? 1) m and n are integers 2) mn=15

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