Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Jul 2010
Posts: 76

Is the integer n odd? [#permalink]
Show Tags
01 Jun 2011, 14:43
1
This post received KUDOS
5
This post was BOOKMARKED
Question Stats:
60% (01:09) correct 40% (01:31) wrong based on 207 sessions
HideShow timer Statistics
Is the integer n odd? (1) n^22n is not a multiple of 4 (2) n is a multiple of 3 They say that n(n2) becomes divisible by 4 as soon as n is even, so n must be odd. Well what about n=2? >Isn't n^22n=0, an even integer? Did Manhattan Gmat forget about that option?
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by heyholetsgo on 02 Jun 2011, 03:16, edited 2 times in total.





Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: What about 0? [#permalink]
Show Tags
01 Jun 2011, 14:52
heyholetsgo wrote: Is the integer n odd? 1.) n^22n 2.) n is a multiple of 3 Well what about n=2? > n^22n=0, an even integer? Did Manhattan Gmat forget about that option? Guess you missed the RHS in statement 1: 1.) n^22n=0 \(n^22n=0\) \(n(n2)=0\) Thus, Either n=2 or n=0. Both are even. We can conclusively say that "No, n is not odd" Sufficient. 2) n can be 3 OR n can be 6. Not Sufficient. Ans: "A"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Feb 2011
Posts: 703

Re: What about 0? [#permalink]
Show Tags
01 Jun 2011, 15:52
1. Sufficient
n^22n =0
=> n=0 or n =2
in both the situations n is not odd and enough to answer the question
2. Not sufficient
as n can be 0 or 3 or 6 or 9....
Answer is A.



Manager
Joined: 05 Jul 2010
Posts: 182

Re: What about 0? [#permalink]
Show Tags
01 Jun 2011, 18:13
Yes, Clear A. B can be odd and even.



Manager
Joined: 06 Jul 2010
Posts: 76

Re: What about 0? [#permalink]
Show Tags
02 Jun 2011, 03:15
Uhhh, I'm sorry guys, forgot a tiny but important part of the question.... They say that n(n2) becomes divisible by 4 as soon as n is even, so n must be odd. But I believe n could be 2 such that the result is even > 0.



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: What about 0? [#permalink]
Show Tags
02 Jun 2011, 03:37
heyholetsgo wrote: Uhhh, I'm sorry guys, forgot a tiny but important part of the question.... They say that n(n2) becomes divisible by 4 as soon as n is even, so n must be odd. But I believe n could be 2 such that the result is even > 0. Oh!!! n^22n will be divisible by 4 for all even n's. But statement 1 says that the expression is not divisible by 4. Thus, "n" is definitely not even; all integers are either even or odd; if n is not even, it is odd. Thus, the answer to the question is: Yes, "n" is odd. And statement 1 is sufficient. **************************** If n=2; n(n2)=2*0=0; "0" is divisible by 4. Thus, n=2 doesn't fit well with the condition given in statement 1. Note: 0 is even. 0 is divisible by all real numbers but 0 itself. 0 is a multiple of all real numbers.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 06 Jul 2010
Posts: 76

Re: What about 0? [#permalink]
Show Tags
02 Jun 2011, 05:18
Damn, 0 is divisible by 4. Thanks man;)



Intern
Joined: 16 Oct 2011
Posts: 27
GMAT 1: 640 Q44 V35 GMAT 2: 720 Q47 V42

Re: What about 0? [#permalink]
Show Tags
19 Oct 2011, 00:35
fluke wrote: Note: 0 is even. 0 is divisible by all real numbers but 0 itself. 0 is a multiple of all real numbers. Is this correct? I would have thought a number is even only if it is divisible by 2 without there being any remainder. *Edit* I retract my question. Since even+even=even, zero must be an even number. Sorry for the confusion!
_________________
GMAT 720 Q47 V42 AWA 6.0, TOEFL 110.



Current Student
Joined: 18 Mar 2011
Posts: 43

Re: What about 0? [#permalink]
Show Tags
20 Oct 2011, 22:55
hey
but how can u equate statement 1 to zero ? Its not given rite ?
Am I missing some thing silly ?



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: What about 0? [#permalink]
Show Tags
20 Oct 2011, 23:48
Priyanka2011 wrote: hey
but how can u equate statement 1 to zero ? Its not given rite ?
Am I missing some thing silly ? We can't equate it to 0. My first reply was to an incomplete question. My second reply was the valid one. Please ignore: whatabout114534.html#p928398Valid reply: whatabout114534.html#p928609
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 26 Sep 2013
Posts: 216
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

Is the integer n odd? (1) n^2 – 2n is not a multiple of 4. [#permalink]
Show Tags
13 Nov 2013, 10:45
Is the integer n odd? (1) \(n^2\) – 2n is not a multiple of 4. (2) n is a multiple of 3. (1) SUFFICIENT:\(n^2\) – 2n = n(n – 2). If n is even, both terms in this product will be even, and the product will be divisible by 4. Since n2 – 2n is not a multiple of 4, we know that the integer n cannot be even—it must be odd.
(2) INSUFFICIENT: Multiples of 3 can be either odd or even. Here's my question: With regards to (1), n could be 2, in which case 2(22)=0, in which case the expression is not a multiple of 4, but n is even. Thus shouldn't the answer be E?



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: Is the integer n odd? (1) n^2 – 2n is not a multiple of 4. [#permalink]
Show Tags
13 Nov 2013, 10:51
AccipiterQ wrote: Here's my question: With regards to (1), n could be 2, in which case 2(22)=0, in which case the expression is not a multiple of 4, but n is even. Thus shouldn't the answer be E?
0 is a multiple of every integer except zero itself.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Math Expert
Joined: 02 Sep 2009
Posts: 43893

Re: Is the integer n odd? (1) n^2 – 2n is not a multiple of 4. [#permalink]
Show Tags
13 Nov 2013, 10:53
AccipiterQ wrote: Is the integer n odd? (1) \(n^2\) – 2n is not a multiple of 4. (2) n is a multiple of 3. (1) SUFFICIENT:\(n^2\) – 2n = n(n – 2). If n is even, both terms in this product will be even, and the product will be divisible by 4. Since n2 – 2n is not a multiple of 4, we know that the integer n cannot be even—it must be odd.
(2) INSUFFICIENT: Multiples of 3 can be either odd or even. Here's my question: With regards to (1), n could be 2, in which case 2(22)=0, in which case the expression is not a multiple of 4, but n is even. Thus shouldn't the answer be E? Merging similar topics.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 04 Oct 2013
Posts: 176
Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30 GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)

Re: Is the integer n odd? (1) n^2 – 2n is not a multiple of 4. [#permalink]
Show Tags
07 Jan 2014, 01:38
2
This post received KUDOS
1. \(n^22n\) is not a multiple of 4. follows \(n(n2)\)is not a multiple of 4 find out in which points the equation yields zero, zero is a multiple of 4 as well as a multiple of any number except zero itself. value a=0 and value b=2 thus n must not be any of those two values because otherwise the expression would result in a multiple of 4 n can be both positive or negative, the only restriction is that n is an integer since o and 2 are out of the pool 4 would be the first positive even number applicable to n. Every other positive even number would cause the expression to be a multiple of 4. We can safely say that n is for sure not an even number. before submitting the answer let's quickly check how the expression behaves with negatives. if n=2 the greatest negative even integer plugged \(n^22n\) results in a multiple of 4 then for sure n is odd. Sufficient. 2. n is a multiple of 3. Non sufficient, n could be zero.
_________________
learn the rules of the game, then play better than anyone else.



Current Student
Joined: 21 Oct 2013
Posts: 193
Location: Germany
GPA: 3.51

Re: Is the integer n odd? [#permalink]
Show Tags
23 Jan 2014, 23:39
1
This post was BOOKMARKED
(1) n²2n ==> n(n2) = 0. Thus, n = 2 or n = 0. Both are multiples of 4. Every other even integer (also the negatives) result in a multiple of 4. Thus n is clearly odd. You could also just plug in numbers....
(2) n is a multiple of 3 > clearly IS. could be 6 or 9 or 12 or 15 and so on.



NonHuman User
Joined: 09 Sep 2013
Posts: 13790

Re: Is the integer n odd? [#permalink]
Show Tags
07 Jul 2015, 02:13
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



SVP
Joined: 08 Jul 2010
Posts: 1956
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Is the integer n odd? [#permalink]
Show Tags
07 Jul 2015, 13:34
heyholetsgo wrote: Is the integer n odd?
(1) n^22n is not a multiple of 4 (2) n is a multiple of 3
Given : n is an IntegerQuestion : Is n odd?Statement 1: n^22n is not a multiple of 4i.e. n(n2) is a multiple of 4 but since n and (n2) are separated by 2 therefore, they will both be either even or both be odd Since the product is even so they must be even. Hence SUFFICIENTStatement 2: n is a multiple of 3a multiple of 3 may be even (e.g. 6 or 12) or may be odd (e.g. 3 or 9). Hence, NOT SUFFICIENTAnswer: Option A
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 03 Aug 2015
Posts: 62
Concentration: Strategy, Technology

Re: Is the integer n odd? [#permalink]
Show Tags
26 Jan 2016, 06:40
GMATinsight wrote: heyholetsgo wrote: Is the integer n odd?
(1) n^22n is not a multiple of 4 (2) n is a multiple of 3
Given : n is an IntegerQuestion : Is n odd?Statement 1: n^22n is not a multiple of 4i.e. n(n2) is a multiple of 4 but since n and (n2) are separated by 2 therefore, they will both be either even or both be odd Since the product is even so they must be even. Hence SUFFICIENTStatement 2: n is a multiple of 3a multiple of 3 may be even (e.g. 6 or 12) or may be odd (e.g. 3 or 9). Hence, NOT SUFFICIENTAnswer: Option A Very good explanation....Thx +1 Kudos



Director
Joined: 26 Oct 2016
Posts: 682
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: Is the integer n odd? [#permalink]
Show Tags
22 Feb 2017, 11:38
We don't need to know which value n might be, just whether n is odd. Therefore, do not rephrase this question to “What is integer n?” Doing so unnecessarily increases the amount of information we need to answer the question. Of course, if you happen to know what n is, then great, you can answer any Yes/No question about n. But you generally don't need to know the value of n to answer Yes/No questions about n. (1) SUFFICIENT: n^2 – 2n = n(n – 2). If n is even, both terms in this product will be even, and the product will be divisible by 4. Since n^2 – 2n is not a multiple of 4, we know that the integer n cannot be even—it must be odd. (2) INSUFFICIENT: Multiples of 3 can be either odd or even. Hence A.
_________________
Thanks & Regards, Anaira Mitch




Re: Is the integer n odd?
[#permalink]
22 Feb 2017, 11:38






