x+y+z is even, is x*y*z even? 1) x*y even 2) y*z odd : DS Archive
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# x+y+z is even, is x*y*z even? 1) x*y even 2) y*z odd

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x+y+z is even, is x*y*z even? 1) x*y even 2) y*z odd [#permalink]

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10 May 2005, 19:35
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x+y+z is even, is x*y*z even?
1) x*y even
2) y*z odd
VP
Joined: 14 Feb 2005
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10 May 2005, 22:51
x+y+z is even, is x*y*z even?

This is always true..bcos for X+Y+Z to be true

one case : two of the three variable have to be odd and one even

second case : All the three have to be even...

so x*y*z will always be even.....

Please check the question and let us know
VP
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10 May 2005, 22:57
Ozmba2006 wrote:
x+y+z is even, is x*y*z even?

This is always true..bcos for X+Y+Z to be true

one case : two of the three variable have to be odd and one even

second case : All the three have to be even...

so x*y*z will always be even.....

Please check the question and let us know

the question doesnt state that x and y and z have to be integers...
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VP
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11 May 2005, 01:22
Agree with Christophe.

However, and to to asnwer the question, I will consider that x,y and z are considered as integers.

1) x*y even
if XY is even, XYZ is always even.
it doesn't matter if Z is odd or even because any number multiplied by any even number = EVEN
suff

2) y*z odd which means both numbers are odd
We know that x+y+z is even so the only way for this to be right is if Z is even because y(odd) +z (odd) + x (even) = even number
Then we have XYZ -> X(even)*Y(odd)*Z(odd) = EVEN
suff
VP
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11 May 2005, 01:48
C)...

1) x=2 and y=1 and z=1 YES x=4 and y=1/2 and z=3/2 NO

2) y=1 and z=3 and x=2 YES y=1/2 and z=10 and x=3/2 NO

1) and 2) x and y and z must be integers for the statements to be true
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11 May 2005, 01:48
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