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

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Manager
Joined: 06 Apr 2010
Posts: 74
x+y+z is even, is x*y*z even?  [#permalink]

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16 Jun 2010, 22:50
4
00:00

Difficulty:

95% (hard)

Question Stats:

20% (02:27) correct 80% (01:26) wrong based on 132 sessions

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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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Joined: 02 Sep 2009
Posts: 48067

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19 Jun 2010, 13:17
4
2
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.

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Manager
Joined: 30 May 2010
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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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Concentration: Strategy, General Management
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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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Joined: 05 Mar 2010
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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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Joined: 07 Jun 2010
Posts: 48
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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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Joined: 12 May 2010
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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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Joined: 12 May 2010
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19 Jun 2010, 13:27
u r right. nice one. tnx
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Joined: 16 Aug 2018
Posts: 17
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
Re: x+y+z is even, is x*y*z even?  [#permalink]

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20 Aug 2018, 01:04
i've never seen a gmat question like this. you'll only see it in gmatclub.
odd/even questions typically get involved with integers only.
i've done many tests on gmatclub forum. a lot of them do not seem to be a gmat question although their difficulty level is 700+. it's critical to focus on the scope of gmat questions.
Re: x+y+z is even, is x*y*z even? &nbs [#permalink] 20 Aug 2018, 01:04
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