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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] New post 10 Apr 2008, 00:53
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

1. wx + yz is odd
2. wz + xy is odd

Pls. give me your reasoning! Thanks
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Re: Odd logic [#permalink] New post 10 Apr 2008, 02:10
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I remember this one from GMAT Prep2....

B

My reasoning:

1. wx + yz is odd ---> we have to possible options: even+odd and odd+even. Let consider even+odd option. wx=even. What can we say about w/x? for w=2, x=2, w/x is odd but for w=4, x=2, w/x is even. Therefore, the first condition is insufficient.

2. wz + xy is odd.

Let make a transformation of w/x + y/z

w/x + y/z = (wz+xy)/xz

The second condition says that nominator is odd. therefore, w/x + y/z can be odd or fraction. The last case we have to exclude because w/x and y/z are integers.
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Re: Odd logic [#permalink] New post 10 Apr 2008, 05:31
great explanation. But why did you transform the statement for the 2nd one and not the first one?

Did you notice that the first statement had the 2 int divided in the same term?

Any frankly when approaching problems why didnt you just go plug in and test for the 2nd statement? What made you think of combining the statement? I guess that is my problem. I would have immediately went towards the brute force approach. How long do you just look at a DS problem before putting pen to paper?
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Re: Odd logic [#permalink] New post 10 Apr 2008, 05:49
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I always try to solve DS in my mind. Here it is the case when I did not use a pen. In my opinion logic is more reliable approach than putting numbers for odd/even problems. I remember that I tried to solve the second condition by the same approach as the first one but failed. After that I made a step back and looked at the problem and the second condition to find what is a key....And answer became obvious. :wink:
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Re: Odd logic [#permalink] New post 10 Apr 2008, 09:13
sondenso wrote:
If w, x, y and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

1. wx + yz is odd
2. wz + xy is odd

Pls. give me your reasoning! Thanks



B. Just think about it.

Only way for WX+YZ to be odd is if and only if either WX or YZ are odd. Both cannot be odd or even. 1 must be completely odds. Thus that means W*X or Y*Z both of one of these are odd.

However we could have 3 of the variables as odds.

Ex/ 12/4+3/1 or just 12/3+3/1 thus we have a Y and N situation.


2: Again one of these must be odd. Thus WZ or XY are odd and W and Z or X and Y are both odd.

Notice that something changes here though. We must have a third odd in this case. Because we cannot have an odd number in the numerator divided by an even number in the denominator... This will not result in an integer!!!

Thus we have 3 odds. Doesnt matter which of the variables, but just notice that. Thus we have O/O+E/O ---> O+Even. We have an odd number.
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Re: Odd logic [#permalink] New post 10 Apr 2008, 19:05
Thank you all, I got it.
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Re: Odd logic   [#permalink] 10 Apr 2008, 19:05
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