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

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Manager
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Joined: 22 Feb 2007
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x is the sum of y consecutive integers. w is the sum of z [#permalink] New post 24 Mar 2007, 10:27
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

A way to solve this w/o picking #s but following mathematical rules?
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Re: sum of consecutive integers [#permalink] New post 24 Mar 2007, 16:41
amd08 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

A way to solve this w/o picking #s but following mathematical rules?


Is it C?

took the general form of consequtive nymbers like n-1,n,n+1
Senior Manager
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 [#permalink] New post 24 Mar 2007, 17:42
Choices (A) and (B) are clear if we take x = 1+2+..+6 = 21 and w = 6+7+8 = 21 or w = 1+2+3 = 6. Also (D) and (E) can be proved TRUE while picking some numbers. :)

(C) x/y means average-mean...so here it can not be an integer since the number of terms is an even number (y = 2z) and there is a property of mean of consecutive integers:

The average of even number of consecutive terms or integers CAN NOT be an an integer.

Answer should be (C).
  [#permalink] 24 Mar 2007, 17:42
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