Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Feb 2010
Posts: 201

If m and n are integers, is m odd? [#permalink]
Show Tags
14 Jul 2010, 13:44
1
This post received KUDOS
20
This post was BOOKMARKED
Question Stats:
64% (00:53) correct 36% (01:02) wrong based on 465 sessions
HideShow timer Statistics
If m and n are integers, is m odd? (1) n + m is odd (2) n + m = n^2 + 5
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 16 Feb 2010
Posts: 201

Re: m odd? [#permalink]
Show Tags
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=10+5= 6 thus even if n=1, m=11+5 = 5 thus odd... what am i missing?



CEO
Joined: 17 Nov 2007
Posts: 3511
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: m odd? [#permalink]
Show Tags
14 Jul 2010, 13:55
(1) n,m could be odd,even ore even,odd. insufficient (2) m = n^2  n + 5 or m = oddeven  oddeven + 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=10+5= 6 thus even if n=1, m=11+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 musthave app especially if you aim at 700+  PrepGame



Manager
Joined: 16 Feb 2010
Posts: 201

Re: m odd? [#permalink]
Show Tags
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 = oddeven  oddeven + 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=10+5= 6 thus even if n=1, m=11+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: 44599

Re: m odd? [#permalink]
Show Tags
14 Jul 2010, 14:07
9
This post received KUDOS
Expert's post
6
This post was BOOKMARKED



Current Student
Joined: 09 Jul 2013
Posts: 25
Location: United States (WA)
GPA: 3.65
WE: Military Officer (Military & Defense)

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
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: \(m  5 = n^2  n\) \(m  5 = n(n  1)\) \(m = n(n1) +5\) m = Even + odd. Therefore, m is odd.
n(n1) 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*(31) = 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.



Senior Manager
Joined: 03 Dec 2012
Posts: 305

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



Manager
Joined: 03 Dec 2013
Posts: 62

Re: m odd? [#permalink]
Show Tags
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 > \(m5=n^2n\) > \(m5=n(n1)\), either \(n\) or \(n1\) is even hence \(n(n1)=even\) > \(m5=modd=even\) > \(m=odd\). 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 + (5m) = 0  > is a quadratic equation with sum of roots = 1 and product of roots = (5m). 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 (5m) is also even. For (5m) to be even, m must be odd. Sufficient! Answer: B



Senior Manager
Joined: 20 Dec 2013
Posts: 254
Location: India

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
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(n1)=m5 Now n(n1) is a product of 2 consecutive integers so it'll definitely be even=>m5=even So m=odd because only oddodd=even Ans option B
Posted from my mobile device



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11500
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
14 May 2015, 17:02
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: 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
CoFounder & 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!***********************



VP
Joined: 09 Jun 2010
Posts: 1222

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



Current Student
Joined: 18 Oct 2014
Posts: 886
Location: United States
GPA: 3.98

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



Intern
Joined: 26 Jul 2016
Posts: 22
Concentration: Finance, Strategy
WE: Analyst (Energy and Utilities)

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
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(1n) = 5 n(1n) {can say one is odd other is even like consecutive numbers} :. m + n(1n) [even] = 5 [odd] This is only possible when m is odd as Odd + Even = Odd Hence (B)



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2582
GRE 1: 323 Q169 V154

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
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(n1)+5 here n(n1) is a product of two consecutive integers. hence it must be even so n=even+5 => even+odd => odd hence sufficient hence B
_________________
Getting into HOLLYWOOD with an MBA The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)Average GRE Scores At The Top Business Schools!



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3396
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

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



Senior Manager
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance

Re: If m and n are integers, is m odd? [#permalink]
Show Tags
08 Dec 2017, 02:27
(1) M+N = O either M or O can be Odd Insuff (2) n^2n=MO n(n1)+O=M n(n1) are two consecutive integers hence their product will always be an EVEN number E+O=O=M
M is an ODD number
Answer B




Re: If m and n are integers, is m odd?
[#permalink]
08 Dec 2017, 02:27






