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If w,x,y and z are distinct positive integers such that

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If w,x,y and z are distinct positive integers such that [#permalink] New post 26 Aug 2006, 10:24
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If w,x,y and z are distinct positive integers such that w+x+y+z=150, which of the following must be true?

(I) If the three sums w+x, y+z and w+z are all even, at least one of {w,x,y,z} is greater than 40.
(II) If x/(w+y+z) > y/(x+w+z), x>y.
(III) If w,x, and y are factors of z, z is either 80 or 144.

Last edited by kevincan on 26 Aug 2006, 12:51, edited 1 time in total.
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 [#permalink] New post 26 Aug 2006, 12:42
I seems unclear, could you clarify this part "f w+x and y+z w+z are all even"
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 [#permalink] New post 26 Aug 2006, 13:00
I - means x y z w are all odd, or all even. Couldn't find a combo in even integers that had all below 40. So this is true...
II - Also seems to be true... Componendo rule? Also tried with numeric examples
III - :shock:
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Re: PS: distinct positive integers [#permalink] New post 26 Aug 2006, 13:05
kevincan wrote:
If w,x,y and z are distinct positive integers such that w+x+y+z=150, which of the following must be true?

(I) If w+x and y+z w+z are all even, at least one of {w,x,y,z} is greater than 40.
(II) If x/(w+y+z) > y/(x+w+z), x>y.
(III) If w,x, and y are factors of z, z is either 80 or 144.


I and II are true but not sure about III. confirm later.

Quote:
(I) If (w+x), (y+z) and (w+z) are all even, at least one of {w,x,y,z} is greater than 40.
Re: PS: distinct positive integers   [#permalink] 26 Aug 2006, 13:05
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