It is currently 22 Nov 2017, 02:53

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If m and n are integers, is m odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 218

Kudos [?]: 378 [1], given: 16

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

Show Tags

New post 14 Jul 2010, 13:44
1
This post received
KUDOS
16
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:10) correct 39% (01:11) wrong based on 438 sessions

HideShow timer Statistics

If m and n are integers, is m odd?

(1) n + m is odd
(2) n + m = n^2 + 5
[Reveal] Spoiler: OA

Kudos [?]: 378 [1], given: 16

Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 218

Kudos [?]: 378 [0], given: 16

Re: m odd? [#permalink]

Show Tags

New post 14 Jul 2010, 13:46
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?

Kudos [?]: 378 [0], given: 16

Expert Post
3 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4670 [3], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member
Re: m odd? [#permalink]

Show Tags

New post 14 Jul 2010, 13:55
3
This post received
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

Kudos [?]: 4670 [3], given: 360

Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 218

Kudos [?]: 378 [0], given: 16

Re: m odd? [#permalink]

Show Tags

New post 14 Jul 2010, 13:57
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

Kudos [?]: 378 [0], given: 16

Expert Post
10 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42302

Kudos [?]: 133014 [10], given: 12402

Re: m odd? [#permalink]

Show Tags

New post 14 Jul 2010, 14:07
10
This post received
KUDOS
Expert's post
5
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.

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133014 [10], given: 12402

Current Student
avatar
B
Joined: 09 Jul 2013
Posts: 25

Kudos [?]: 20 [0], given: 15

Location: United States (WA)
Schools: Foster '18 (M)
GMAT 1: 710 Q44 V44
GPA: 3.65
WE: Military Officer (Military & Defense)
Reviews Badge
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 16 Aug 2013, 06:22
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.

Kudos [?]: 20 [0], given: 15

Senior Manager
Senior Manager
User avatar
Joined: 03 Dec 2012
Posts: 329

Kudos [?]: 188 [0], given: 291

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

Show Tags

New post 23 Nov 2013, 05:04
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

Kudos [?]: 188 [0], given: 291

Manager
Manager
avatar
Joined: 03 Dec 2013
Posts: 64

Kudos [?]: 91 [0], given: 35

Re: m odd? [#permalink]

Show Tags

New post 28 Mar 2014, 01:11
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

Kudos [?]: 91 [0], given: 35

Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 267

Kudos [?]: 108 [0], given: 29

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

Show Tags

New post 28 Mar 2014, 08:22
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

Kudos [?]: 108 [0], given: 29

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15564

Kudos [?]: 283 [0], given: 0

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

Show Tags

New post 12 May 2015, 02:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10158

Kudos [?]: 3530 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 14 May 2015, 17:02
1
This post received
KUDOS
Expert's post
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


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3530 [1], given: 173

VP
VP
avatar
S
Joined: 09 Jun 2010
Posts: 1393

Kudos [?]: 168 [0], given: 916

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

Show Tags

New post 15 May 2015, 00:48
very tricky, I missed this question.

not hard but enough to kill us
_________________

visit my facebook to help me.
on facebook, my name is: thang thang thang

Kudos [?]: 168 [0], given: 916

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15564

Kudos [?]: 283 [0], given: 0

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

Show Tags

New post 02 Jun 2016, 05:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

1 KUDOS received
Current Student
User avatar
Joined: 18 Oct 2014
Posts: 903

Kudos [?]: 436 [1], given: 69

Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 02 Jun 2016, 10:25
1
This post received
KUDOS
zisis wrote:
If m and n are integers, is m odd?

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


1) n + m is odd
It can be odd+even or even +odd. m can be even or odd. Not sufficient.

(2) n + m = n^2 + 5

Let's suppose n is odd, n^2 will also be odd. Hence to maintain the equality m must be odd.

Let's suppose n is even, n^2 will be even. And to maintain the equality m must be odd.

B is the answer
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Kudos [?]: 436 [1], given: 69

Intern
Intern
avatar
Joined: 26 Jul 2016
Posts: 24

Kudos [?]: 7 [0], given: 42

Concentration: Finance, Strategy
WE: Analyst (Energy and Utilities)
GMAT ToolKit User
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 11 Oct 2016, 05:07
zisis wrote:
If m and n are integers, is m odd?

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



A) m + n = odd
Two possibilities :-
1- m is odd and n is even : 1 + 2 = 3
2- m is even and n is odd : 2 + 1 = 3
Two possibilities, :. Insufficient

B) m+n = n^2 + 5

Solve

m + n - n^2 = 5
m + n(1-n) = 5
n(1-n) {can say one is odd other is even like consecutive numbers}

:. m + n(1-n) [even] = 5 [odd]

This is only possible when m is odd
as Odd + Even = Odd

Hence (B)

Kudos [?]: 7 [0], given: 42

Retired Moderator
avatar
P
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 876 [0], given: 602

GMAT ToolKit User Premium Member
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 21 Nov 2016, 11:15
Great Question
Here we are given two integers m,n
And we are asked if m is odd or not
Statement 1
m+n=odd
hmm
This Statement just tells us that m and n are of opposite even/odd nature
Not sufficient
Statement 2
m=n(n-1)+5
here n(n-1) is a product of two consecutive integers. hence it must be even
so n=even+5 => even+odd => odd
hence sufficient
hence B
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 876 [0], given: 602

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3102

Kudos [?]: 1116 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If m and n are integers, is m odd? [#permalink]

Show Tags

New post 21 Nov 2016, 11:28
zisis wrote:
If m and n are integers, is m odd?

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


FROM STATEMENT - I ( INSUFFICIENT )

If n + m = Odd

Either n = Odd/Even and m = Odd/Even because -

1. Even + Odd = Odd
2. Odd + Even = Odd

FROM STATEMENT - II ( INSUFFICIENT )

n - n^2 = 5 - m

Or, n ( n - 1 ) = 5 - m

Here, LHS must be Even, because product of 2 consecutive integers is always even ( ie, one of the 2 consecutive numbers must be even )

So, 5 - m = Evem

Or, Odd - m = Even

Hence, m = Odd

Thus, Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked, answer will certainly be (B)...

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1116 [0], given: 327

Re: If m and n are integers, is m odd?   [#permalink] 21 Nov 2016, 11:28
Display posts from previous: Sort by

If m and n are integers, is m odd?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.