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Is N an even number? [#permalink]
 08 Nov 2012, 04:11
Question Stats:
39% (01:38) correct
60% (01:42) wrong based on 38 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
Last edited by Bunuel on 08 Nov 2012, 04:21, edited 1 time in total.
Edited the question.
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Re: Is N an even number? [#permalink]
08 Nov 2012, 04:38
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.
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Re: Is N an even number? [#permalink]
21 Apr 2013, 09:15
Even i get the answer as D someone please clarify , is D the right answer ?
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Re: Is N an even number? [#permalink]
21 Apr 2013, 13:42
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.
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Re: Is N an even number? [#permalink]
24 Apr 2013, 18:25
In D.S the number zero is very important. If you take that into consideration A gets eliminated. B is the Answer.
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Re: Is N an even number? [#permalink]
27 Apr 2013, 14:47
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?
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Last edited by smyarga on 28 Apr 2013, 02:49, edited 2 times in total.
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Re: Is N an even number? [#permalink]
27 Apr 2013, 15:32
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
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Re: Is N an even number? [#permalink]
27 Apr 2013, 16:25
Statement 1 with a set of consecutive numbers such as -2, -1, 0, 1, 2. SufficientStatement 2 is 1 + 2^2 + 3^2+ 4^2 + 5^2 = 55. SufficientAnswer is DProbably either statement 1 is mis-stated or answer is wrong
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Re: Is N an even number? [#permalink]
27 Apr 2013, 19:56
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.
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Re: Is N an even number? [#permalink]
28 Apr 2013, 02:14
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.
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Re: Is N an even number? [#permalink]
28 Apr 2013, 03:01
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
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Re: Is N an even number? [#permalink]
29 Apr 2013, 16:44
if N==0 than A fails because 0 is not an even or odd integer.
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Re: Is N an even number? [#permalink]
29 Apr 2013, 22:29
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.
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Re: Is N an even number? [#permalink]
30 Apr 2013, 01:09
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Re: Is N an even number? [#permalink]
30 Apr 2013, 10:30
thanks bunnel. I need to revise quant.
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Re: Is N an even number? [#permalink]
30 Apr 2013, 21:25
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 .....
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Re: Is N an even number? [#permalink]
06 May 2013, 13:14
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.
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Re: Is N an even number? [#permalink]
07 May 2013, 03:47
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 .................
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Re: Is N an even number? [#permalink]
07 May 2013, 12:08
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 .
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Re: Is N an even number? [#permalink]
08 May 2013, 00:10
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!
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Re: Is N an even number?
[#permalink]
08 May 2013, 00:10
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