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Consecutive integers

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Manager
Joined: 25 May 2009
Posts: 140
Concentration: Finance
GMAT Date: 12-16-2011

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09 Jul 2009, 20:37
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0% (00:00) correct 100% (04:08) wrong based on 3 sessions

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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

OA=C

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Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1243
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34

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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
Posts: 757
Location: New Delhi
WE 1: 5.5 yrs in IT

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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: 757
Location: New Delhi
WE 1: 5.5 yrs in IT

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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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