Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Dec 2013, 12:21

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is N an even number?

Author Message
TAGS:
Intern
Joined: 07 Nov 2012
Posts: 15
Followers: 0

Kudos [?]: 4 [0], given: 10

Is N an even number? [#permalink]  08 Nov 2012, 03:11
00:00

Difficulty:

45% (medium)

Question Stats:

37% (01:37) correct 62% (01:31) wrong based on 72 sessions
Is N an even number?

(1) The average of N consecutive integers is zero.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Nov 2012, 03:21, edited 1 time in total.
Edited the question.
Intern
Joined: 07 Nov 2012
Posts: 15
Followers: 0

Kudos [?]: 4 [0], given: 10

Re: Is N an even number? [#permalink]  08 Nov 2012, 03:38
I have posted this one because I get answer D and can't see how it can be B

(1) The average of N consecutive integers is zero.

For the average to be zero, the set must straddle zero ie. -2, -1, 0, 1, 2 = average zero. Therefore in this case 5 integers, therefore N is not even. To straddle zero the set must always contain an odd number of integers. Sufficient.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

1 + 4 + 9 + 16 + 25 = 55. Therefore N = 5 and is not even. Sufficient.

The answer I have is B. What am I missing for point one? Why is it not sufficient? The only explanation I can think of is that the 'average' of zero consecutive integers is zero, and zero is an even integer, therefore not sufficient. Though this explanation hardly seems plausible.
Intern
Joined: 23 Jan 2013
Posts: 38
Concentration: Technology, Other
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: Is N an even number? [#permalink]  21 Apr 2013, 08:15
Even i get the answer as D someone please clarify , is D the right answer ?
Manager
Joined: 27 Feb 2012
Posts: 141
Followers: 1

Kudos [?]: 8 [0], given: 22

Re: Is N an even number? [#permalink]  21 Apr 2013, 12:42
shelrod007 wrote:
Even i get the answer as D someone please clarify , is D the right answer ?

I agree the OA should be certainly D.
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Senior Manager
Joined: 21 Jan 2010
Posts: 345
Followers: 0

Kudos [?]: 49 [0], given: 12

Re: Is N an even number? [#permalink]  24 Apr 2013, 17:25
In D.S the number zero is very important. If you take that into consideration A gets eliminated. B is the Answer.
Intern
Joined: 20 Apr 2012
Posts: 40
Location: Ukraine
GMAT 1: 690 Q51 V31
WE: Education (Education)
Followers: 5

Kudos [?]: 40 [0], given: 10

Re: Is N an even number? [#permalink]  27 Apr 2013, 13:47
Quote:
In D.S the number zero is very important. If you take that into consideration A gets eliminated. B is the Answer.

May be I can be wrong, but if N=0, we will have that the average of elements from empty set is 0. This not true. How can we find the average of nothing?! Should we add nothing and divide by 0, because the number of elements is 0? definitely you can't consider average of elements from empty set. Here definitely should be D. What is the source of this question?
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

Last edited by smyarga on 28 Apr 2013, 01:49, edited 2 times in total.
Intern
Joined: 18 Nov 2011
Posts: 40
Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: Is N an even number? [#permalink]  27 Apr 2013, 14:32
derekgmat wrote:
I have posted this one because I get answer D and can't see how it can be B

(1) The average of N consecutive integers is zero.

For the average to be zero, the set must straddle zero ie. -2, -1, 0, 1, 2 = average zero. Therefore in this case 5 integers, therefore N is not even. To straddle zero the set must always contain an odd number of integers. Sufficient.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

1 + 4 + 9 + 16 + 25 = 55. Therefore N = 5 and is not even. Sufficient.

The answer I have is B. What am I missing for point one? Why is it not sufficient? The only explanation I can think of is that the 'average' of zero consecutive integers is zero, and zero is an even integer, therefore not sufficient. Though this explanation hardly seems plausible.

The answer you have is D, both are sufficient. B would mean only the second is sufficient
Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 178
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 31 [0], given: 65

Re: Is N an even number? [#permalink]  27 Apr 2013, 15:25
Statement 1 with a set of consecutive numbers such as -2, -1, 0, 1, 2. Sufficient

Statement 2 is 1 + 2^2 + 3^2+ 4^2 + 5^2 = 55. Sufficient

Probably either statement 1 is mis-stated or answer is wrong
_________________

KUDOS is a way to say Thank You

Intern
Joined: 14 Apr 2013
Posts: 11
Followers: 0

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

Re: Is N an even number? [#permalink]  27 Apr 2013, 18:56
derekgmat wrote:
I have posted this one because I get answer D and can't see how it can be B

(1) The average of N consecutive integers is zero.

For the average to be zero, the set must straddle zero ie. -2, -1, 0, 1, 2 = average zero. Therefore in this case 5 integers, therefore N is not even. To straddle zero the set must always contain an odd number of integers. Sufficient.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

1 + 4 + 9 + 16 + 25 = 55. Therefore N = 5 and is not even. Sufficient.

The answer I have is B. What am I missing for point one? Why is it not sufficient? The only explanation I can think of is that the 'average' of zero consecutive integers is zero, and zero is an even integer, therefore not sufficient. Though this explanation hardly seems plausible.

Hi derekgmat,
I think the answer should be B, please find below my analysis

1) The average of N consecutive integers is zero.

The average can be 0 if we have the numbers as -3, 0, 3. N is odd here.
The average can be 0 if we have the numbers as -3, -1, 1, 3. N is even here.

Thus statement 1 is not sufficient enough to guess if N is even or odd.

2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

1 + 4 + 9 + 16 + 25 = 55. Therefore N = 5 and is not even. Sufficient.
_________________

Regards,
Fugitive

Intern
Joined: 20 Apr 2012
Posts: 40
Location: Ukraine
GMAT 1: 690 Q51 V31
WE: Education (Education)
Followers: 5

Kudos [?]: 40 [0], given: 10

Re: Is N an even number? [#permalink]  28 Apr 2013, 01:14
Quote:
Hi derekgmat,
I think the answer should be B, please find below my analysis

1) The average of N consecutive integers is zero.

The average can be 0 if we have the numbers as -3, 0, 3. N is odd here.
The average can be 0 if we have the numbers as -3, -1, 1, 3. N is even here.

Thus statement 1 is not sufficient enough to guess if N is even or odd.

2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

1 + 4 + 9 + 16 + 25 = 55. Therefore N = 5 and is not even. Sufficient.

-3, -1, 1, 3 are not consecutive integers. You missed 0.
-3, 0, 3 are not consecutive integers.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

Intern
Joined: 14 Apr 2013
Posts: 11
Followers: 0

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

Re: Is N an even number? [#permalink]  28 Apr 2013, 02:01
Thanks Smyarga for pointing out. It seems I was in a hurry and missed the word 'consecutive' in the statement...

You guys are correct OA should be D
_________________

Regards,
Fugitive

Senior Manager
Joined: 21 Jan 2010
Posts: 345
Followers: 0

Kudos [?]: 49 [0], given: 12

Re: Is N an even number? [#permalink]  29 Apr 2013, 15:44
if N==0 than A fails because 0 is not an even or odd integer.
Intern
Joined: 20 Apr 2012
Posts: 40
Location: Ukraine
GMAT 1: 690 Q51 V31
WE: Education (Education)
Followers: 5

Kudos [?]: 40 [0], given: 10

Re: Is N an even number? [#permalink]  29 Apr 2013, 21:29
Bluelagoon wrote:
if N==0 than A fails because 0 is not an even or odd integer.

0 is an even integer because it divisible by 2.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

Math Expert
Joined: 02 Sep 2009
Posts: 15211
Followers: 2560

Kudos [?]: 15825 [0], given: 1572

Re: Is N an even number? [#permalink]  30 Apr 2013, 00:09
Expert's post
Bluelagoon wrote:
if N==0 than A fails because 0 is not an even or odd integer.

Zero 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 (in fact zero is divisible by every integer except zero itself).

Hope it's clear.
_________________
Senior Manager
Joined: 21 Jan 2010
Posts: 345
Followers: 0

Kudos [?]: 49 [0], given: 12

Re: Is N an even number? [#permalink]  30 Apr 2013, 09:30
thanks bunnel. I need to revise quant.
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 96
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 57 [0], given: 11

Re: Is N an even number? [#permalink]  30 Apr 2013, 20:25
derekgmat wrote:
Is N an even number?

(1) The average of N consecutive integers is zero.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

Question asks Is N = Even ??

Stmt - 1 :: The average of N consecutive integers is zero. However as we know the average of Even number of consecutive integers can never be an integer. Therefore, Straight NO . . Hence, Sufficient ..

Stmt - 2 :: The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55. Calculate it manually, as

1^2+ 2^2+3^2+4^2+5^2 \Rightarrow 1+4+9+16+25 = 55. Hence, N = Odd.
Sufficient.

Hence, D .....
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Senior Manager
Joined: 21 Jan 2010
Posts: 345
Followers: 0

Kudos [?]: 49 [0], given: 12

Re: Is N an even number? [#permalink]  06 May 2013, 12:14
Is N an even number?

(1) The average of N consecutive integers is zero.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

More thoughts :
The avg of N consecutive integers is 0. N is odd for all cases except when 0 is the only number in the set. The statement 1 if 0 is the only statement reads :
The average of zero consecutive integers is zero. Mathematically is is correct. But than 0 is an even number. Hence Insufficient.

B gives the anser.

hence B.
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 96
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 57 [0], given: 11

Re: Is N an even number? [#permalink]  07 May 2013, 02:47
derekgmat wrote:
Is N an even number?

(1) The average of N consecutive integers is zero.

(2) The sum of the first N perfect squares 1^2 + 2^2 + .... + N^2 = 55

Pls review the OA as I must be D .................
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

SVP
Joined: 05 Jul 2006
Posts: 1554
Followers: 4

Kudos [?]: 48 [0], given: 39

Re: Is N an even number? [#permalink]  07 May 2013, 11:08
I think D is the right choice

for N consecutive intigers , if n is even then their sum is definitely not divisible by n (i.e. the median or the mean dosn't exist in the set ) and since 0 is an integer then surely sum of n is devisable by n and thus n is odd. this means that 0 exists in the set and it is the middle term .
Intern
Joined: 05 Feb 2013
Posts: 17
Location: Ukraine
GMAT 1: 660 Q50 V28
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: Is N an even number? [#permalink]  07 May 2013, 23:10
Guys, clearly we have within the statement 1 only the following options:
N=1 , so average 0/1= 0 , thus N odd

OR

A set of consecutive integers such as:

-1, 0, 1
-2,-1,0,1,2
etc.....
Hence, in order to sutisfy statement 1 , N is ALLWAYS odd -----> sufficient!

definitely D!
Re: Is N an even number?   [#permalink] 07 May 2013, 23:10
Similar topics Replies Last post
Similar
Topics:
1) An even number of marbles, call it "N", are distributed 3 19 May 2004, 10:11
what is the range of n consecutive even positive numbers 3 22 Jan 2005, 19:18
The sum of the even numbers between 1 and n is 79*80, where 2 25 Jan 2005, 12:48
The sum of the even numbers between 1 and n is 79*80, where 7 25 May 2005, 12:47
h(n) is the product of the even numbers from 2 to n, 3 14 Oct 2007, 18:17
Display posts from previous: Sort by