Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 27 Apr 2015, 16:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If m and n are integers, is m odd?

Author Message
TAGS:
Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 112 [0], given: 16

If m and n are integers, is m odd? [#permalink]  14 Jul 2010, 12:44
4
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:04) correct 46% (01:04) wrong based on 157 sessions
If m and n are integers, is m odd?

(1) n + m is odd
(2) n + m = n^2 + 5
[Reveal] Spoiler: OA
Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 112 [0], given: 16

Re: m odd? [#permalink]  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?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2133 [2] , given: 359

Re: m odd? [#permalink]  14 Jul 2010, 12:55
2
KUDOS
Expert's post
(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.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 112 [0], given: 16

Re: m odd? [#permalink]  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
Math Expert
Joined: 02 Sep 2009
Posts: 27123
Followers: 4189

Kudos [?]: 40505 [6] , given: 5540

Re: m odd? [#permalink]  14 Jul 2010, 13:07
6
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Intern
Joined: 09 Jul 2013
Posts: 19
Location: United States
Schools: Wharton '17, Haas '17
GMAT 1: 710 Q44 V44
GMAT 2: Q V
GPA: 3.65
WE: Military Officer (Military & Defense)
Followers: 0

Kudos [?]: 12 [0], given: 10

Re: If m and n are integers, is m odd? [#permalink]  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.

Senior Manager
Joined: 03 Dec 2012
Posts: 367
Followers: 0

Kudos [?]: 51 [0], given: 291

Re: If m and n are integers, is m odd? [#permalink]  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.
Manager
Joined: 03 Dec 2013
Posts: 68
Followers: 0

Kudos [?]: 24 [0], given: 35

Re: m odd? [#permalink]  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.

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!
Senior Manager
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 57 [0], given: 29

Re: If m and n are integers, is m odd? [#permalink]  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

Posted from my mobile device
Re: If m and n are integers, is m odd?   [#permalink] 28 Mar 2014, 07:22
Similar topics Replies Last post
Similar
Topics:
5 If p, m, and n are positive integers, n is odd, and p = m^2 6 24 Feb 2014, 07:44
2 Is the product of integers m and n odd? 4 09 Oct 2013, 18:56
3 If m, n, and p are integers, is m + n odd? 5 26 Jun 2013, 08:22
1 If m and n are integers, is m odd? 4 16 Aug 2009, 14:26
If m & n are integers, is m odd? 1.) n+m is odd 2.) n+m 5 16 Oct 2006, 18:46
Display posts from previous: Sort by