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x+y+z is even, is x*y*z even?

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x+y+z is even, is x*y*z even? [#permalink] New post 16 Jun 2010, 21:50
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x+y+z is even, is x*y*z even?

(1) x*y even
(2) y*z odd

How does one answer if the variables are not specified as integers? Does gmat try to sneak in this kind of question? thanks!
P/S : I don't know the OA
[Reveal] Spoiler: OA
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Re: Odd/even [#permalink] New post 17 Jun 2010, 08:27
In order for a number to be even or odd, it must be an integer.
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Re: Odd/even [#permalink] New post 18 Jun 2010, 21:38
I hate such questions!! :x

If x+y+z is even, & xyz are integers then in any case xyz will also be even. But the question has given us two options, hence assuming that x,y & z are not integers or not all integers. e.g x=3.5 y=4.5 z=2 or vice versa.

I think its "C"
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Re: Odd/even [#permalink] New post 19 Jun 2010, 03:15
Here's my solution

any even or odd number is an integer.

Given condition -> x+y+z = even, so only two possibles either 2 of them are odd and one is even, or all three are even

Stmt 1 - considering both the possibilities, if x*y is even means withe x can be odd or y can be even or vice versa, or both can be even. Now if z is odd or even, the result will be an even integer. SUFFICIENT

Stmt 2 - y*z is odd, means both should be odd. That means x is even (to satisfy given condition). the result will be an even integer. SUFFICIENT

I will go with D

Whts the OA?
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Re: Odd/even [#permalink] New post 19 Jun 2010, 10:34
x+y+z is even, is x*y*z even?
1) x*y even
2) y*z odd

x+y+z = even , here we have 4 scenarios

1. E + E + E
2. O + O + E
3. O + e + O
4. E + O + O

(I) X * Y = EVEN

SO WE HAVE FOLLOWING POSSIBILITIES
X Y
EVEN EVEN
EVEN ODD
ODD EVEN

SO CLEARLY 1 IS INSUFFI

(2) Y*Z = ODD

Y Z
ODD ODD


SO CLEARLY 2 IS INSUFFI

SO COMBINING BOTH MEANS EVEN ODD ODD WE CAN SOLVE

ANS C
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Re: Odd/even [#permalink] New post 19 Jun 2010, 11:50
you r wrong. for a yes/no que the answer is d.
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Re: Odd/even [#permalink] New post 19 Jun 2010, 12:17
Expert's post
Eden wrote:
x+y+z is even, is x*y*z even?
1) x*y even
2) y*z odd

How does one answer if the variables are not specified as integers? Does gmat try to sneak in this kind of question? thanks!
P/S : I don't know the OA


Note that we are not told that x, y, and z are integrs.

Given: x+y+z=even. Question: xyz=even?

(1) xy=even --> if x=\frac{4}{5}, y=5 and z=\frac{1}{5}
(xy=even=4, x+y+z=6=even), then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

(2) yz=odd --> again if x=\frac{4}{5}, y=5 and z=\frac{1}{5}
(yz=odd=1, x+y+z=6=even), then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

(1)+(2) the same here: if x=\frac{4}{5}, y=5 and z=\frac{1}{5}, then the answer would be NO as xyz=\frac{4}{5}\neq{integer} but if x=0 and y+z=any \ odd+any \ odd=some \ even, then the answer would be YES. Not sufficient.

Answer: E.
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Re: Odd/even [#permalink] New post 19 Jun 2010, 12:27
u r right. nice one. tnx
Re: Odd/even   [#permalink] 19 Jun 2010, 12:27
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