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# if w, x, y, and z are integers such that w/x and y/z are

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Intern
Joined: 17 Jul 2006
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if w, x, y, and z are integers such that w/x and y/z are [#permalink]

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17 Sep 2006, 12:20
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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)wy + xy is odd

the answer is B. however, i dont understand why statement 1 is not suff. can someone please explain?
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Joined: 05 Jul 2006
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17 Sep 2006, 12:52
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)wy + xy is odd

from stem either w/x is odd and y/z even or the opposite ...for them to be odd

lets see together

from one

wx+yz is odd thus either wx is even and thus yz is odd or the opposite.

if wx is odd thus both w,x are odd and in the same time

yz will be even and thus either y or z OR BOTH ARE EVEN , NOTE THAT (from stem y/z intiger then if one of them is even it must be y because odd/even = fraction.

THUS w/x IS SURE ODD BUT Y/Z COULD BE EVEN OR ODD

IF Y EVEN AND Z IS ODD = ODD BUT IF BOTH EVEN THEN THE RESULT MIGHT BE EVEN OR ODD.........INSUFF

eg y= 12 z = 3 , y/z = 4 even but if y = 12,z= 4 or 2 y/z could be 3 or 6

from 2)

y ( w+x) = odd thus y is odd and w is even and x is odd, y/z is intiger

thus z must be odd
... suff

i say it is B

I hope this helps
ok   [#permalink] 17 Sep 2006, 12:52
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