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by abhasjha » Mon Feb 08, 2010 3:34 am
If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

a. wx + yz = odd


b. wz + xy = odd
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by harsh.champ » Mon Feb 08, 2010 4:05 am
abhasjha wrote:If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

a. wx + yz = odd


b. wz + xy = odd
IMO B.



We have to check whether (wz + xy)/xz is odd or not.
Now, considering (2) wz + xy is odd .
Since w/x and y/z is integer =>w/x + y/z should also be an integer.

Now, odd/even is never an integer so the ans. is odd.
Considering (1) we cant prove the upper equality
Last edited by harsh.champ on Mon Feb 08, 2010 4:47 am, edited 2 times in total.
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by shashank.ism » Mon Feb 08, 2010 4:38 am
harsh your solution is not very clear will you please explain it in detail..
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by ajith » Tue Feb 09, 2010 1:10 am
abhasjha wrote:If w, x, y, and z are integers such that w/x and y/z are integers, is w/x + y/z odd?

a. wx + yz = odd


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

If a number's numerator is odd the denominator has to be odd and the result will be odd (if the result is an integer)
Odd/Odd = Odd

So B is sufficient

A is not sufficient
[spoiler]
B[/spoiler]
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