Consecutive integers

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Joined: 25 May 2009

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Consecutive integers [#permalink]

09 Jul 2009, 20:37

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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

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Kudos [?]: 383 [0], given: 156

Re: Consecutive integers [#permalink]

09 Jul 2009, 22:56

Now this is a type of question which I am always shy of (I hope after these early days of my preparation, it will be over)

The only solution in my mind is to solve it by putting integers therein.

If any one has some different way to solve it, kindly let me know.

I have tried it but am stuck!!

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Director

Joined: 03 Jun 2009

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Kudos [?]: 277 [0], given: 56

Re: Consecutive integers [#permalink]

09 Jul 2009, 23:38

IMO C

Given that y = 2z.
This means, y is an even number,
i.e. x is the sum of y consecutive integers, where y is even.

Now, remember that - average of n consecutive numbers, where n is even, is always a non-integer value (in the form of __.5)

C is x/y, i.e. average of consecutive numbers, hence non-integer.
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Director

Joined: 03 Jun 2009

Posts: 806

Location: New Delhi

WE 1: 5.5 yrs in IT

Followers: 46

Kudos [?]: 277 [0], given: 56

Re: Consecutive integers [#permalink]

09 Jul 2009, 23:43

another method of substituting values (by hit and trial) and POE:

A. x = w, possible for x=1+2+3+4+5+6, and w=6+7+8
B. x > w, certainly possible, if we use big numbers for x
C. x/y is an integer (leave this one for time being)
D. w/z is an integer, possible, w=1+2+3 and z=3
E. x/z is an integer, possible, x=1+2+3+4+5+6, and z=3

Hence C
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Re: Consecutive integers [#permalink] 09 Jul 2009, 23:43

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Consecutive integers

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