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# Is the sum of six consecutive integers even? 1. The first

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Intern
Joined: 15 Apr 2003
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Is the sum of six consecutive integers even? 1. The first [#permalink]  05 Aug 2003, 10:45
Is the sum of six consecutive integers even?

1. The first integer is odd

2. The average of six integers is odd

Can someone evaluate stment 2?

I get that stment two does not even make sense b/c if you take the avg of any 6 consec integers you will get a non-integer. I figured this by saying that the integers are x, x+1, x+2, x+3, x+4, x+5 and the avg is
(6x+15)/6

However someone said that stment 2 is suff b/c:

avg = (sum of the 6 intergers)/6. Thus if the avg is an odd number then
the sum must be even since an odd number * 6 is even. Thus we know sum is even and stment 2 is sufficient.

Did I do something wrong or is the answer to this Q really A.
Manager
Joined: 22 Jul 2003
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My choice will be E.

Sum of any 6 consecutive numbers is an odd number.
Avg is a fraction not an integer.
Intern
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Let me give a try on stmt 2

(6n+15)/6 = 2k+1

=> 6n + 15 = 12k + 6
=> 12k-6n = 9
=> 2k - n = 3/2

Since k & n are integers this would not be possible. Hence Stmt 2 fails .

Am I correct in this approach
Director
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Looks like a poorly prepared question!
Where did you get the question from?
GMAT Instructor
Joined: 07 Jul 2003
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Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Re: Data Sufficiency Help [#permalink]  05 Aug 2003, 22:58
numlock31 wrote:
Is the sum of six consecutive integers even?

1. The first integer is odd

2. The average of six integers is odd

Can someone evaluate stment 2?

I get that stment two does not even make sense b/c if you take the avg of any 6 consec integers you will get a non-integer. I figured this by saying that the integers are x, x+1, x+2, x+3, x+4, x+5 and the avg is
(6x+15)/6

However someone said that stment 2 is suff b/c:

avg = (sum of the 6 intergers)/6. Thus if the avg is an odd number then
the sum must be even since an odd number * 6 is even. Thus we know sum is even and stment 2 is sufficient.

Did I do something wrong or is the answer to this Q really A.

This question must be wrong. Any six consecutive integers will always be an odd number because you have 3 odds and 3 evens no matter what. Since the question can be answered without ANY of the choices, the question must be wrong, The only way that this question would make sense is if the number of integers was odd, say 5.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Re: Data Sufficiency Help   [#permalink] 05 Aug 2003, 22:58
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