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If m and n are integers, is m odd?

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If m and n are integers, is m odd? [#permalink] New post 14 Jul 2010, 12:44
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If m and n are integers, is m odd?

(1) n + m is odd
(2) n + m = n^2 + 5
[Reveal] Spoiler: OA
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Re: m odd? [#permalink] New post 14 Jul 2010, 12:46
zisis wrote:
if m and n are integers, is m odd?

(1) n+m is odd
(2) n+m = n^2 + 5



1 is insuf
2 is insuf for me

let me explain:
m = n^2 - n + 5
thus, if n =0, m=1-0+5= 6 thus even
if n=1, m=1-1+5 = 5 thus odd...

what am i missing?
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Re: m odd? [#permalink] New post 14 Jul 2010, 12:55
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(1) n,m could be odd,even ore even,odd. insufficient

(2) m = n^2 - n + 5 or m = odd|even - odd|even + odd = (odd - odd)|(even - even) + odd = even + odd = odd. sufficient.

zisis wrote:
if m and n are integers, is m odd?

let me explain:
m = n^2 - n + 5
thus, if n =0, m=1-0+5= 6 thus even
if n=1, m=1-1+5 = 5 thus odd...

what am i missing?


0^2 = 0.
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Re: m odd? [#permalink] New post 14 Jul 2010, 12:57
walker wrote:
(1) n,m could be odd,even ore even,odd. insufficient

(2) m = n^2 - n + 5 or m = odd|even - odd|even + odd = (odd - odd)|(even - even) + odd = even + odd = odd. sufficient.

zisis wrote:
if m and n are integers, is m odd?

let me explain:
m = n^2 - n + 5
thus, if n =0, m=1-0+5= 6 thus even
if n=1, m=1-1+5 = 5 thus odd...

what am i missing?


0^2 = 0.





aaaaaaaaaaaaaaaaaaaaaaaaaa
it s the other way round
2^0 = 1 and not 0^2 = 1
aaaaaaaaaa
going mental
thanks
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Re: m odd? [#permalink] New post 14 Jul 2010, 13:07
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If m and n are integers, is m odd?

(1) n + m is odd --> \(n+m=odd\). The sum of two integers is odd only if one is odd and another is even, hence \(m\) may or may not be odd. Not sufficient.

(2) n + m = n^2 + 5 --> \(m-5=n^2-n\) --> \(m-5=n(n-1)\), either \(n\) or \(n-1\) is even hence \(n(n-1)=even\) --> \(m-5=m-odd=even\) --> \(m=odd\). Sufficient.

Answer: B.
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Re: If m and n are integers, is m odd? [#permalink] New post 16 Aug 2013, 05:22
m and n are integers, is m odd?
-Can't rephrase the question here, so you work with m = odd? It's a Yes/No DS question type.

Here's how I approached the problem.

Statement 1.
Given: m + n is odd.
Using even/odd number property rules:
even + odd = odd. OR, odd + even = odd. Since m can be either even or odd in this case, Statement 1 is insufficient, we don't have enough information.

Statement 2.
Given: \(m+n = n^2 + 5\)

Simplifying the equation:
\(m - 5 = n^2 - n\)
\(m - 5 = n(n - 1)\)
\(m = n(n-1) +5\)
m = Even + odd. Therefore, m is odd.

n(n-1) will always be even because it's a number times the number preceding it (think consecutive)...so one of those numbers has to be even (if n = 3 for example, you would have 3*(3-1) = 3*(2) = 6). You have an even*odd = even situation here.

5 is odd. So putting it all together, m = Even + Odd. You can answer with the given information that, yes, m is odd. Sufficient.

So the answer is B.
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Re: If m and n are integers, is m odd? [#permalink] New post 23 Nov 2013, 04:04
Statement 1, m and n could be both odd or one odd, one even. Insufficient.
Statement 2, when n is odd, n^2+5 is even, then m+n is even, m is odd; when n is even, n^2+5=odd, m+n is odd,
then m is odd. Sufficient.
So, answer is B
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Re: m odd? [#permalink] New post 28 Mar 2014, 00:11
Bunuel wrote:
If m and n are integers, is m odd?

(1) n + m is odd --> \(n+m=odd\). The sum of two integers is odd only if one is odd and another is even, hence \(m\) may or may not be odd. Not sufficient.

(2) n + m = n^2 + 5 --> \(m-5=n^2-n\) --> \(m-5=n(n-1)\), either \(n\) or \(n-1\) is even hence \(n(n-1)=even\) --> \(m-5=m-odd=even\) --> \(m=odd\). Sufficient.
Answer: B.


Another method:
St1: n + m is odd, Answer is YES when n is even but answer is NO when n is odd.
Insufficient!

St2: n + m = n^2 + 5 --> n^2 - n + (5-m) = 0 -- > is a quadratic equation with sum of roots = 1 and product of roots = (5-m). Clearly the the roots are consecutive integers with least among them as negative (ex. 4 & -3, 6 & -5...) That means one of the root is even. So, product of roots (5-m) is also even. For (5-m) to be even, m must be odd.
Sufficient!
Answer: B
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Re: If m and n are integers, is m odd? [#permalink] New post 28 Mar 2014, 07:22
Satatment 1:Clearly insuff.
Even+odd=odd.So m could be even or odd.
S2:sufficient.
The eq can be rearranged as
N(n-1)=m-5
Now n(n-1) is a product of 2 consecutive integers so it'll definitely be even=>m-5=even
So m=odd because only odd-odd=even
Ans option B

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Re: If m and n are integers, is m odd? [#permalink] New post 12 May 2015, 01:17
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Re: If m and n are integers, is m odd? [#permalink] New post 14 May 2015, 16:02
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Hi All,

Even though this is an old post (and most of the original posters are probably long gone), this question serves as a nice example of some of the Number Properties that you're likely to face on Test Day. If you can spot the NPs involved, then you can move relatively quickly through the work, but even if you don't recognize the NPs, you can still TEST VALUES to prove that patterns exist. In that way, you can do some quick work and avoid "staring at the screen" and hoping that something comes to you.

We're told that M and N are INTEGERS. We're asked if M is ODD. This is a YES/NO question.

Fact 1: N + M is ODD

IF....
N = 1
M = 0
The answer to the question is NO

IF....
N = 0
M = 1
The answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: N + M = N^2 + 5

Here, the value of M depends on the value of N. Let's start with something simple and see if a pattern emerges.

IF....
N = 0
M = 5
The answer to the question is YES

IF....
N = 1
M = 5
The answer to the question is YES

IF....
N = 2
M = 7
The answer to the question is YES

IF....
N = 3
M = 11
The answer to the question is YES

It certainly looks like the answer to the question is ALWAYS YES. We can quickly TEST some negative values for N and see what happens....

IF....
N = -1
M = 7
The answer to the question is YES

IF....
N = -2
M = 11
The answer to the question is YES
Fact 2 is SUFFICIENT

Final Answer:
[Reveal] Spoiler:
B


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Re: If m and n are integers, is m odd? [#permalink] New post 14 May 2015, 23:48
very tricky, I missed this question.

not hard but enough to kill us
Re: If m and n are integers, is m odd?   [#permalink] 14 May 2015, 23:48
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