x is the sum of y consecutive integers. w is the sum of z : PS Archive
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# x is the sum of y consecutive integers. w is the sum of z

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x is the sum of y consecutive integers. w is the sum of z [#permalink]

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03 Apr 2008, 14:49
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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

Spoiler: _____C______
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03 Apr 2008, 17:08
fresinha12 wrote:
A..

X cannot be equal to w..

y is 2,3,4,5,6,7: x=27
z is 8,9,10: w=27

sum of consecutive integers is always indivisible by the number of integers if the number of integers is even.
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03 Apr 2008, 18:10
yes..C it is..
grrr..stupid careless mistake....grrr

NOTE to SELF read the damn freakin question CAREFULLY
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03 Apr 2008, 19:10
neelesh 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

C. y is always an even number but z could or could not be. in such case, x/y cannot yeild an integer. the question is "could be". so z could be an odd integer but y is always an even integer.
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06 Apr 2008, 19:31
how about 0,1,2 . The sum of that is 3 (x) and they are three consecutive integers (y).

So, x/y is an integer. No ?
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07 Apr 2008, 09:23
sum of even number of consecutive integers is always odd. Since y is even, x/y is not an integer
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03 May 2008, 13:26
What if:
z=2 then y=2z=2.2=4
x is then the sum of 4 consecutive integers x=1+2+3+4=10
w is then the sum of 2 consecutive integers w=7+8=15

A) x=w? x=10 w=15 No
B) x>w? 10>15 No
C) x/y integer? 10/4 No
D) w/z integer? 15/2 No
E) x/z integer? 10/2 Yes
Can anyone explain to me why this is wrong?
Thanks

Sorry, I found my mistake!
Re: PS: Consecutive sums   [#permalink] 03 May 2008, 13:26
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