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could be true EXCEPT - Sleak question

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could be true EXCEPT - Sleak question

by logitech » Sun Dec 07, 2008 3:47 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
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by pbanavara » Sun Dec 07, 2008 6:09 pm
Is it 1 ? x=w

I just tried trial and error and spent almost 4 minutes.. so I guess I'm wrong

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Re: could be true EXCEPT - Sleak question

by hwiya320 » Sun Dec 07, 2008 6:15 pm
logitech 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
x = w?

x>w: x can be greater than w since there are more Ys than Z.
x/y is an integer: if z was odd, and y being always even, there can be an integer
w/z is an integer: 4+5+6 = 15/3 = integer, true
x/z is an integer: if z can be even or odd, so they can divide sum of some consecutive numbers..

please explain if there are easier explanation
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by dmateer25 » Sun Dec 07, 2008 6:29 pm
Well since we can determine that y will always be even.

Let's say there are 2 integers.

x = 5+6 = 11

11/4 is not an integer

let's say there are 4 integers.

x = 1+2+3+4 = 10

10/4 is not an integer

let's say there are 6 integers.

x=1+2+3+4+5+6 = 21

21/6 is not an integer.

This always holds true.

I believe that the sum of an even number of consecutive integers will never be a multiple of the number of integers.

x/y will never be an integer.
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by vittalgmat » Sun Dec 07, 2008 7:31 pm
Logitech,
I need some clarification here. x and y are +ve ints => implies that the sum is a +ve number. The individual ints can be + or -ve.

right?
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by earth@work » Sun Dec 07, 2008 8:05 pm
IMO:C
let a & b be any integers positive or negative, let (a+1), (a+2),..... & (b+1),(b+2),..... be two sets of consecutive nos
x=(a+1)+(a+2)+.....+(a+y)=(a+1)+(a+2)+...+(a+2z)
x=2az+z(2z+1)....................................................(1)
w=(b+1)+(b+2)+...(b+z)=bz+z(z+1)/2.......................(2)
x/y is an integer div equation(1) by 2z, CANNOT be true as z(2z+1) divided 2z does not give integer value as 2z+ will be always odd.

We can also check for other values:
w/z is an integer , divide eqn (2) by z,cud be true if z is odd.
x/z is an integer this is true
x = w put equation(1)=(2) we get z=(b-2a)*2, cud be true as we cud get positive integer value of z by plugging in values of a&b i.e a=1b=5 we get z=6
x > w by this we get inequality z>(b-2a)*2, which cud be true by plugging in values of a & b
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by logitech » Mon Dec 08, 2008 12:26 am
Great work earth@work!

OA is C
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by hwiya320 » Mon Dec 08, 2008 5:40 am
Ok, I have to ask logitech.

Why is your target score so low? not that 680 is not a low score, but looking at your contribution to this forum, it seems like you can target much higher?
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by logitech » Mon Dec 08, 2008 9:10 am
hwiya320 wrote:Ok, I have to ask logitech.

Why is your target score so low? not that 680 is not a low score, but looking at your contribution to this forum, it seems like you can target much higher?
680 + Logitech = My Dream School

780 + Logitech = My Dream School + 100

I am not greedy. And remember it is one of the 7 sins! :D
LGTCH
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