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# Is the sum of a series of n consecutive integers even? I) n

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Manager
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Is the sum of a series of n consecutive integers even? I) n [#permalink]  18 Jan 2008, 09:10
1
KUDOS
Is the sum of a series of n consecutive integers even?

I) n = 6

II) The n digit number formed by the series is a multiple of nine.
Director
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Re: Consecutive integers [#permalink]  18 Jan 2008, 09:19
Skewed wrote:
Is the sum of a series of n consecutive integers even?

I) n = 6

II) The n digit number formed by the series is a multiple of nine.

1 is sufficient (the sum is always odd, there will always be 3 odd and 3 even numbers their sum is odd)
2 is irrelevant 4,5 (sum is odd); 3,4,5,6 (sum is even).
Manager
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Re: Consecutive integers [#permalink]  18 Jan 2008, 10:09
I think A is the Answer.

maratikus wrote:
Skewed wrote:
Is the sum of a series of n consecutive integers even?

I) n = 6

II) The n digit number formed by the series is a multiple of nine.

1 is sufficient (the sum is always odd, there will always be 3 odd and 3 even numbers their sum is odd)
2 is irrelevant 4,5 (sum is odd); 3,4,5,6 (sum is even).
Senior Manager
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Re: Consecutive integers [#permalink]  18 Jan 2008, 11:25
A too because of the same reasons
Manager
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Re: Consecutive integers [#permalink]  18 Jan 2008, 12:24
Well, I agree w/ A.

The OA says D though - "Using the rules of divisibility, we can see that if the n digit number formed by the series is a multiple of nine then the sum of its digits must be divisible by nine. Therefore the sum of its digits must also be odd."

Think the OA is incorrect..

For the number to be divisible by 9, the sum of its digits has to be divisible by nine, but that doesn't mean that the sum is only odd. e.g 108 is divisible by 9 b/c the sum of its digits is 9 which is odd. 4185 is also divisible by 9 b/c the sum of its digits is 18 which is even.

Am i missing anything??
CEO
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Re: Consecutive integers [#permalink]  18 Jan 2008, 14:19
Skewed wrote:
Is the sum of a series of n consecutive integers even?

I) n = 6

II) The n digit number formed by the series is a multiple of nine.

1: suff. We have O+E +O+E + O+E --> O+O+O --> Odd

2: Insuff.

A.

Can you double check to see if you posted all the information??? Thanks
Manager
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Re: Consecutive integers [#permalink]  18 Jan 2008, 16:23
Nah man, I double-checked before posting.
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Re: Consecutive integers [#permalink]  18 Jan 2008, 18:12
Skewed wrote:
Well, I agree w/ A.

The OA says D though - "Using the rules of divisibility, we can see that if the n digit number formed by the series is a multiple of nine then the sum of its digits must be divisible by nine. Therefore the sum of its digits must also be odd."

Think the OA is incorrect..

For the number to be divisible by 9, the sum of its digits has to be divisible by nine, but that doesn't mean that the sum is only odd. e.g 108 is divisible by 9 b/c the sum of its digits is 9 which is odd. 4185 is also divisible by 9 b/c the sum of its digits is 18 which is even.

Am i missing anything??

Yeah, you missed nothing, but OA wrong! A for me too
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Re: Consecutive integers   [#permalink] 18 Jan 2008, 18:12
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