Is n^2 an even integer? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 20 Jan 2017, 21:21

### 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

# Is n^2 an even integer?

Author Message
TAGS:

### Hide Tags

Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 513
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Followers: 26

Kudos [?]: 747 [2] , given: 630

Is n^2 an even integer? [#permalink]

### Show Tags

01 Nov 2013, 23:56
2
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

51% (02:22) correct 49% (01:23) wrong based on 116 sessions

### HideShow timer Statistics

Is n^2 an even integer?

(1) n/2 is an odd integer.

(2) (n^2)/2 is not an even integer.

GH-06.12.13 | OE to follow
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36583
Followers: 7087

Kudos [?]: 93289 [3] , given: 10555

Re: Is n^2 an even integer? [#permalink]

### Show Tags

02 Nov 2013, 03:56
3
KUDOS
Expert's post
Is n^2 an even integer?

Notice that we are NOT told that n is an integer.

(1) n/2 is an odd integer --> $$\frac{n}{2}=odd$$ --> $$n=2*odd=even$$ --> n^2=even^2=even. Sufficient.

(2) (n^2)/2 is not an even integer --> if n=1, then the answer is NO but if $$n=\sqrt{2}$$, then the answer is YES. Not sufficient.

Hope it's clear.
_________________
Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 513
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Followers: 26

Kudos [?]: 747 [0], given: 630

Re: Is n^2 an even integer? [#permalink]

### Show Tags

05 Nov 2013, 21:42
Official Explanation

- Statement (1) is sufficient. If n/2 is an odd integer, we can find n by multiplying both sides by 2. n is 2 times an odd integer, which is always an even. If n is an even, then n^2 is an even -- an even times an even is always an even.

Statement (2) is not sufficient. Note that "not an even integer" does not mean "an odd integer." It could also refer to any non-integer, such as 4.5. If n = 3, then n^2 = 9 and n^2/2 = 4.5, which is not an even integer. In that case, the answer is "no." However, if n^2 = 2, then n^2/2 = 1, which is not an even integer. But in this case, n^2 is even, so the answer is "yes." Choice (A) is correct.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1901
Followers: 49

Kudos [?]: 366 [0], given: 454

Re: Is n^2 an even integer? [#permalink]

### Show Tags

22 Aug 2016, 01:59
Excellent Question
Here we don't know if N is an integer or not
Statement 1 => n/2=odd => n must be an integer and that too even as n=odd*2
suff
Staement 2 => n^2/2≠even =z(say)
Now for z=>
case 1 => let it be odd => n^2 will be even=> YES
case 2 => let it be 4.5 => n^2/2=4.5 => n^2 is odd => NO
case 3 => let it be 3434850948540.324334314343 (anything) clearly here n wont be an integer forget it being odd/even=> NO
hence insuff
Smash that A
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evensand Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

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

Manager
Joined: 13 Jan 2015
Posts: 94
Concentration: Other, General Management
Followers: 0

Kudos [?]: 12 [0], given: 66

Re: Is n^2 an even integer? [#permalink]

### Show Tags

23 Aug 2016, 13:37
I do not agree with A being the answer.
Please correct me if i am wrong

If N = 1/2, then for statement 1

1/2 /2 = 1 which is an odd integer which makes then N^2 is not even
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1901
Followers: 49

Kudos [?]: 366 [1] , given: 454

Re: Is n^2 an even integer? [#permalink]

### Show Tags

23 Aug 2016, 13:42
1
KUDOS
Tmoni26 wrote:
I do not agree with A being the answer.
Please correct me if i am wrong

If N = 1/2, then for statement 1

1/2 /2 = 1 which is an odd integer which makes then N^2 is not even

Hi mate
The mistake you made here is as follows => 1/2 /2 = 1/4 not 1
If x/2=odd integer => x=2*odd now as we know that the product of two integers is always an integer => x is an integer and that too even as 2 is its factor.
Smash that A
_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evensand Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

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

Manager
Joined: 13 Jan 2015
Posts: 94
Concentration: Other, General Management
Followers: 0

Kudos [?]: 12 [0], given: 66

Re: Is n^2 an even integer? [#permalink]

### Show Tags

24 Aug 2016, 01:01
stonecold,

Thanks a lot....
Re: Is n^2 an even integer?   [#permalink] 24 Aug 2016, 01:01
Similar topics Replies Last post
Similar
Topics:
2 If n is a positive integer, is n + 2 > z? 3 17 Mar 2016, 02:59
Is the integer a even? 2 18 Aug 2014, 02:34
8 If k = (n + 2)(n - 2), where n is an integer value greater 5 23 Feb 2014, 13:20
Is N/2 an odd integer? (1) 2N is even (2) N is even 5 27 Feb 2012, 06:04
Is integer N even? 1) N^2=N 2)N=N^3 Statement (1) ALONE is 3 17 Feb 2011, 13:33
Display posts from previous: Sort by