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x+y+z is even, is x*y*z even? [#permalink]
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16 Jun 2010, 22:50
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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
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Re: Odd/even [#permalink]
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17 Jun 2010, 09:27
In order for a number to be even or odd, it must be an integer.



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Re: Odd/even [#permalink]
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18 Jun 2010, 22:38
I hate such questions!! 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]
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19 Jun 2010, 04:15
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]
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19 Jun 2010, 11:34
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]
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19 Jun 2010, 12:50
you r wrong. for a yes/no que the answer is d.



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Re: Odd/even [#permalink]
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19 Jun 2010, 13:17
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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]
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19 Jun 2010, 13:27
u r right. nice one. tnx



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Re: x+y+z is even, is x*y*z even? [#permalink]
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Re: x+y+z is even, is x*y*z even? [#permalink]
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Re: x+y+z is even, is x*y*z even?
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