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# If W,X,Y, and Z are integers such that W/X and Y/Z are

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If W,X,Y, and Z are integers such that W/X and Y/Z are [#permalink]  03 Feb 2006, 23:02
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If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd
(2) WZ + XY is odd
Senior Manager
Joined: 19 Feb 2005
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my guess is (C)
my reasoning is complicated though...I'm not sure

1) WX + YZ = ODD
translate: either WX or YZ is odd, which means at least a couple of numbers is odd, either W&X or Y&Z

2) WZ + XY = ODD
translate: either WZ or XY is odd, which means at least a couple of numbers is odd, either W&Z or X&Y

Combine: 3 are odd and 1 even (will explain more if correct)
It is sufficient to answer NO to the question, because the ratio of an even number to an odd one is EVEN.
VP
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Re: DS - Integers [#permalink]  04 Feb 2006, 06:30
ffgmat wrote:
If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd
(2) WZ + XY is odd

sometime it is easy to plaug in: suppose,
w=6, x=3, y = 5 and z = 1

(1) WX + YZ = 18+5=23, an odd integer. insuff.
(2) WZ + XY = 6+3=9, an odd integer again. insuff.

togather also insuff.
Senior Manager
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Re: DS - Integers [#permalink]  04 Feb 2006, 06:43
Professor wrote:
ffgmat wrote:
If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd
(2) WZ + XY is odd

sometime it is easy to plaug in: suppose,
w=6, x=3, y = 5 and z = 1

(1) WX + YZ = 18+5=23, an odd integer. insuff.
(2) WZ + XY = 6+3=9, an odd integer again. insuff.

togather also insuff.

In this case, you have W/X that is EVEN, so you should also prove that there is a case in which both ratios are ODD, otherwise the answer should be NO, making (1)+(2) sufficient to answer
VP
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Re: DS - Integers [#permalink]  04 Feb 2006, 07:05
thearch wrote:
Professor wrote:
ffgmat wrote:
If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd
(2) WZ + XY is odd

sometime it is easy to plaug in: suppose,
w=6, x=3, y = 5 and z = 1

(1) WX + YZ = 18+5=23, an odd integer. insuff.
(2) WZ + XY = 6+3=9, an odd integer again. insuff.

togather also insuff.

In this case, you have W/X that is EVEN, so you should also prove that there is a case in which both ratios are ODD, otherwise the answer should be NO, making (1)+(2) sufficient to answer

hmm.. make sense, that is what i was looking for. i will look on it in detial later.
Re: DS - Integers   [#permalink] 04 Feb 2006, 07:05
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