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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

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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

A) x = w

B) x > w

C) x/y is an integer

D) w/z is an integer

E) x/z is an integer

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This one is tricky. One way to solve this problem is number crunching but you have to be careful. The crux of this question is the princple that For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms. For example, the sum of 1, 2, and 3 (three consecutives -- an odd number) is 6, which is a multiple of 3. For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms. For example, the sum of 1, 2, 3, and 4 (four consecutives -- an even number) is 10, which is not a multiple of 4.

answered Jun 18, 2014 by Senior Associate (475 points)
what about 45 being the sum of 9 integeres from 1 to 9.

Here x/y is an integer
commented Mar 14, 2016 by Partner (651 points)
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Jyotsna Mehta