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Sum of consecutive integers

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by GmatKiss » Sat Aug 20, 2011 3:46 am
Is the sum of a series of n consecutive integers even?

(1) n=6
(2) The n digit number formed by the seriest is a multiple of nine


OA after some discussion.
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Source: — Data Sufficiency |
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by Frankenstein » Sat Aug 20, 2011 4:01 am
Hi,
From(1):
Sum of integers from a to (a+5) = 6a+15. This is always odd.
Sufficient

From(2):
if the number is 45, sum is odd
if the number is 3456, sum is even
Not sufficient

Hence, A
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by saketk » Sat Aug 20, 2011 9:01 am
GmatKiss wrote:Is the sum of a series of n consecutive integers even?

(1) n=6
(2) The n digit number formed by the seriest is a multiple of nine


OA after some discussion.
Condition 1- any 6 consecutive integers will contain 3 odd and 3 even = resultant will always be ODD.
Sufficient

Condition 2 -- Consider 11+12+13 = 36 -even
Consider 2+3+4+5+6+7 = 27 -- ODD...

Not sufficient.

Hence answer = A
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by Frankenstein » Sat Aug 20, 2011 11:08 am
saketk wrote: Condition 2 -- Consider 11+12+13 = 36 -even
Consider 2+3+4+5+6+7 = 27 -- ODD...

Not sufficient.

Hence answer = A
Hi,
Minor mistake. You cannot choose 11,12,13. If you are choosing this set, you are picking n as 3.
When we write those numbers in a series it becomes 111213, which is not 'n' digit number.
We can only pick single digit numbers.
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by AVbyT » Sat Aug 20, 2011 11:14 am
I didn't understand statement 2. Does it mean that the sum of the n consecutive integers is a multiple of 9?
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by Frankenstein » Sat Aug 20, 2011 11:26 am
AVbyT wrote:I didn't understand statement 2. Does it mean that the sum of the n consecutive integers is a multiple of 9?
Yes, but not directly. If the n consecutive integers are 2,3,4,5,6,7.. then 234567(6- digit number) is divisible by 9. Anyway for a number to be divisible by 9, the sum of its digits should be divisible by 9. So, we can interpret that it says sum of digits is divisible by 9 , but the consecutive numbers chosen should be single digit ones to make the series 'n'- digit number.
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by Thouraya » Thu Sep 15, 2011 10:46 pm
What is the OA for the above question? Thanks
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by sl750 » Fri Sep 16, 2011 7:06 am
Statement 1

n=6

Sum of an even number of consecutive integers is odd when we have an odd number of integers in the sequence, as we have 3 odd and 3 even numbers. The sum is Odd. Sufficient

Statement 2
Depending on whether n is even or odd, the sum of multiples of 9 could be odd/even or even/odd. Insufficient
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