Odd or not

[anticipation]

If y and z are integers, is y × (z + 1) odd?

(1) y is odd
(2) z is even


[spoiler]OA: C[/spoiler]
[spoiler]
Why can't i plugin either of them as zero ? In that case, OA should E. Any inputs to correct my thought process would be great ?[/spoiler]

[selango]

Combining 1 and 2,

y is odd and Z is even

Note that 0 is an even integer.you can plugin the value only for Z.

sub z=0

y(z+1) = y*(0+1)=y

Since y is odd,y(z+1) is odd.

[anticipation]

Combining 1 and 2,

y is odd and Z is even

Note that 0 is an even integer.you can plugin the value only for Z.

sub z=0

y(z+1) = y*(0+1)=y

Since y is odd,y(z+1) is odd.

Thanks for ur inputs. Key here is to know that 0 is even , which I didnt know

[gopal.b]

I could relate to your confusion.

From what I have known since school and also in studies of pure mathematics even and odd numbers were defined by convention only for natural numbers.
Which would mean zero is neither even nor odd and so are all -ve integers.
BUT
the GMAT considers even and odd to be defined for all integers.

All integers of the form 2n where n is an integer are even and all integers of the form 2n+1 where n is an integer are odd.

Which would make 0 even and -2 even and -1 -3 etc odd.

Regards,
Gopal[/quote]