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x is the sum of y consecutive integers. w is the sum of z [#permalink]

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20 Jun 2008, 21:29

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x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

can you solve this problem that is different than the solution from the source of this question?

Re: x is the sum of y consecutive integers [#permalink]

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20 Jun 2008, 22:16

gmatnub wrote:

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

can you solve this problem that is different than the solution from the source of this question?

I am guessing that the answer is A. x cannot equal w because in order for x = w, then the median need for the integers needs to be 0. Since y has an even number of consecutive integers, then it cannot have a median of 0.

Re: x is the sum of y consecutive integers [#permalink]

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21 Jun 2008, 02:10

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The answer should be C, x/y.

Quote:

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

Reasoning: The sum of n consecutive integers is n*(a1+an)/2. So, sum/(number of terms) is integer if and only if (a1+an)/2 is integer which is possible only for odd n. We have y=2z terms, so clearly y is even. So, x/y can’t be an integer.

For any other possibility, we can construct example showing that it could be integer.

Re: x is the sum of y consecutive integers [#permalink]

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21 Jun 2008, 06:56

greenoak wrote:

The answer should be C, x/y.

Quote:

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

Reasoning: The sum of n consecutive integers is n*(a1+an)/2. So, sum/(number of terms) is integer if and only if (a1+an)/2 is integer which is possible only for odd n. We have y=2z terms, so clearly y is even. So, x/y can’t be an integer.

For any other possibility, we can construct example showing that it could be integer.

Re: x is the sum of y consecutive integers [#permalink]

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21 Jun 2008, 07:44

gmatnub wrote:

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

can you solve this problem that is different than the solution from the source of this question?

the point of intrest here is: the mean/median of even number of consecutive integers is/can not an integer.

since z could be odd/even but y can never be odd as it is 2z. if x is sum of y (even) consecutive integers, the mean/median of y consecutive integers cannot be an integer. so x/y is not an integer.
_________________

Re: x is the sum of y consecutive integers [#permalink]

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21 Jun 2008, 22:54

gmatnub wrote:

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

x = w x > w x/y is an integer w/z is an integer x/z is an integer

can you solve this problem that is different than the solution from the source of this question?

Sum of the numbers of a consecutive series is a multiple of the number of terms only when the number of terms is odd and never a multiple when the number of terms is even..