Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39589

If n is an integer, which of the following must be even? [#permalink]
Show Tags
18 Sep 2012, 02:55
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
Question Stats:
94% (01:17) correct
6% (00:14) wrong based on 1523 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
18 Sep 2012, 02:55



Manager
Joined: 25 Jun 2012
Posts: 71
Location: India
WE: General Management (Energy and Utilities)

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
18 Sep 2012, 03:16
1
This post received KUDOS
ans (C) 2n
n=1 => 2n = 2 =>even n=2 => 2n = 4 => even



Director
Joined: 24 Aug 2009
Posts: 503
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
18 Sep 2012, 05:02
1
This post received KUDOS
Answer C Any integer multiplied by an even number will always yield Even integer.
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Manager
Joined: 12 Mar 2012
Posts: 164
Location: India
Concentration: Technology, General Management
GMAT Date: 07232012
WE: Programming (Telecommunications)

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
18 Sep 2012, 06:18
2
This post received KUDOS
Bunuel wrote: If n is an integer, which of the following must be even?
(A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2
Since n is an integer, it can be EVEN or ODD. But any integer when multiplied by 2 is even. For example, 3 * 2 = 6 (even) The rule is: EVEN * ODD = EVEN EVEN * EVEN = EVEN ODD * ODD = ODD A) we cant say as it depends if n is odd or even B) same as A) C) Even as n is multiplied by 2 D) It is ODD as EVEN+1 = ODD E) depends if n is even or odd. Hence C
_________________
FOCUS..this is all I need!
KuDo!



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
21 Sep 2012, 03:37



Intern
Joined: 24 May 2014
Posts: 4

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
24 May 2014, 01:34
1
This post was BOOKMARKED
I thought that an integer could be 0. If that is the case, then 2*(0), would equal 0, which is not equal an even number. Thus, it does not answer the question. Can someone please clarify? Thanks.



Intern
Joined: 30 Jan 2013
Posts: 1

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
24 May 2014, 02:59
Answer: C Any integer multiplied by an even number will always result in an Even integer.



Intern
Joined: 24 May 2014
Posts: 4

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
24 May 2014, 03:13
1
This post received KUDOS
Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.
Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."?



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
24 May 2014, 03:17
momentofzen wrote: Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.
Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."? Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself). I think you should brushup fundamentals on Number Theory: mathnumbertheory88376.htmlAll DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59Hope it helps.
_________________
New to the Math Forum? Please read this: 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



Intern
Joined: 24 May 2014
Posts: 4

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
24 May 2014, 03:31
1
This post received KUDOS
Thank you! I did not realize 0 was considered an even number. Appreciate it. Cheers.



Manager
Joined: 07 Apr 2014
Posts: 141

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
10 Sep 2014, 08:55
1
This post received KUDOS
Bunuel wrote: If n is an integer, which of the following must be even? (A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2 Practice Questions Question: 44 Page: 158 Difficulty: 550 Any integer multiplied by 2 is always even,,, Hence C



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15916

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
22 Dec 2015, 19:29
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



Senior Manager
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 366
Location: United States (CA)
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47
GRE 1: 337 Q168 V169
WE: Education (Education)

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
10 May 2016, 18:02
Attached is a visual that should help.
Attachments
Screen Shot 20160510 at 5.49.39 PM.png [ 53.73 KiB  Viewed 10549 times ]
_________________
Harvard grad and 770 GMAT scorer, offering highquality private GMAT tutoring, both inperson and via Skype, since 2002.
McElroy Tutoring



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1044

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
27 May 2016, 07:24
Bunuel wrote: If n is an integer, which of the following must be even?
(A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2 To solve this question, we need to consider a few odd/even rules. 1) (even + even) or (odd + odd) = even 2) even + odd = odd 3) (even x even) or (even x odd) = even (Note that an even integer times any integer, whether even or odd, will yield an even answer for the product.) 4) odd x odd = odd Doing a quick scan of our answer choices allows us to select C as the correct option. Regardless whether n is even or odd, 2 (which is even) times any integer will always be even. The answer is C.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2884
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
27 May 2016, 08:07
Bunuel wrote: If n is an integer, which of the following must be even? (A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2 Practice Questions Question: 44 Page: 158 Difficulty: 550 Use the property of Even Numbers !! A number is even if it is divisible by 2, among the options given only (C) matches... So, Answer will be (C) IF you want to check you can  n = 2 2n = 4 If n = 3 2n = 6 Thus answer is (C)
_________________
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 )



Intern
Joined: 20 Oct 2015
Posts: 47

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
05 Jul 2016, 03:54
Bunuel wrote: If n is an integer, which of the following must be even? (A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2 Practice Questions Question: 44 Page: 158 Difficulty: 550 I think you forgot about zero In one of the prep author considered "0" neither even nor odd. if we consider "0", which I assume is not, as an even number it would be C



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
05 Jul 2016, 05:47
kamranko wrote: Bunuel wrote: If n is an integer, which of the following must be even? (A) n+1 (B) n+2 (C) 2n (D) 2n +1 (E) n^2 Practice Questions Question: 44 Page: 158 Difficulty: 550 I think you forgot about zero In one of the prep author considered "0" neither even nor odd. if we consider "0", which I assume is not, as an even number it would be C ZERO:1. 0 is an integer. 2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.3. 0 is neither positive nor negative integer (the only one of this kind). 4. 0 is divisible by EVERY integer except 0 itself. Check more here: numberpropertiestipsandhints174996.html
_________________
New to the Math Forum? Please read this: 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



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185

If n is an integer, which of the following must be even? [#permalink]
Show Tags
03 Dec 2016, 18:02
Here as n is an integer > n can be even or odd Notice that 2n is always even
Hence C Additionally 2n+1 is always odd and n and n^2 will have same even/odd nature
_________________
Give me a hell yeah ...!!!!!



Intern
Joined: 23 Oct 2014
Posts: 13

Re: If n is an integer, which of the following must be even? [#permalink]
Show Tags
03 Jan 2017, 06:52
with any integer odd or even multiplied by 2 would be even so option c is correct.........




Re: If n is an integer, which of the following must be even?
[#permalink]
03 Jan 2017, 06:52



Go to page
1 2
Next
[ 22 posts ]





Similar topics 
Author 
Replies 
Last post 
Similar Topics:


2


If n is an integer, which of the following must be an even number? I.

MathRevolution 
6 
04 Apr 2017, 00:03 

4


If a is an odd integer, which of the following must be an even integer

Bunuel 
11 
13 Apr 2017, 01:30 

5


If x is an integer, which of the following must be an even integer?

rbtta23 
3 
13 Apr 2017, 04:01 

7


If n is a positive integer, which of the following must be even? (n −

Bunuel 
3 
13 Apr 2017, 04:29 

21


If x is an even integer, which of the following must be an

slsu 
14 
01 Apr 2016, 01:46 



