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Consecutive Integers

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Consecutive Integers

by heshamelaziry » Mon Nov 16, 2009 5:34 pm
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

OA C [spoiler]Although I learned new concept today about consecutive integers and understand why the answer is indeed correct, I can't refute the other options when I choose variables for each integers in this form: a + a+1+a+2....
for example, to prove a is wrong, the OE simply picked any number of integer, but why when I pick variables it does not work ?[/spoiler]
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by palvarez » Mon Nov 16, 2009 6:23 pm
x = sum of 2z consecutive integers.

x = (2z)*average, here the average is not integer, because the list size is even.
x/y = x/2z = not an integer.

could be true except = must be false. Look for something obvious like the above to zero-in on
Last edited by palvarez on Mon Nov 16, 2009 7:28 pm, edited 1 time in total.
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by heshamelaziry » Mon Nov 16, 2009 7:05 pm
New rule I learned today:

The summ od odd numebr of terms in a set IS a multiple of the number of terms. The sum of an even number of term is NEVER the the multiple of the NUmber of trems. Y + 2Z means y is an even number of terms and consequently x / y is not an integer.
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