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

Question

(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

Bunuel · Accepted Answer

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}
eq{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}
eq{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}
eq{integer}  but if  x=0  and  y+z=any \ odd+any \ odd=some \ even , then the answer would be YES. Not sufficient.

Answer: E.

jpr200012 · Answer

In order for a number to be even or odd, it must be an integer.

Hussain15 · Answer

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"

hardnstrong · Answer

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?

virupaksh2010 · Answer

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

mikioso · Answer

you r wrong. for a yes/no que the answer is d.

mikioso · Answer

u r right. nice one. tnx

shmba · Answer

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.
i wish I were wrong about this.

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

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