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x is the sum of y consecutive integers. w is the sum of z

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Director
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x is the sum of y consecutive integers. w is the sum of z [#permalink] New post 20 Jun 2008, 20:29
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?
Manager
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Re: x is the sum of y consecutive integers [#permalink] New post 20 Jun 2008, 21:16
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.
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Director
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Re: x is the sum of y consecutive integers [#permalink] New post 21 Jun 2008, 01:10
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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.
Manager
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Re: x is the sum of y consecutive integers [#permalink] New post 21 Jun 2008, 05:56
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.

wow, this is a good solution.
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Re: x is the sum of y consecutive integers [#permalink] New post 21 Jun 2008, 06:44
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.
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Re: x is the sum of y consecutive integers [#permalink] New post 21 Jun 2008, 07:41
Answer must be X/Z (i.e., E)

Ex: Z=2, then Y=4

X= Sum of ( 1, 2, 3, 4) = 10
W=Sum of ( 10, 12) = 22

So X/Z= 10/2= 5

Since X has Y numbers in the list and Y=2Z, So obviously X can be divided by Z.
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Re: x is the sum of y consecutive integers [#permalink] New post 21 Jun 2008, 21:54
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..

y = 2z = even..so C is the answer..
Manager
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Re: x is the sum of y consecutive integers [#permalink] New post 24 Jun 2008, 00:18
excellent one! is it mgmat?
Director
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Re: x is the sum of y consecutive integers [#permalink] New post 24 Jun 2008, 08:36
The OA is C, yes it is a mgmat question
Re: x is the sum of y consecutive integers   [#permalink] 24 Jun 2008, 08:36
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