From the question stem we find that x is a factor of z
Stmt I
Either x or z or both of them must be even for their product xz to be even. (Remember the product of two integers is odd only when both of them are odd)
Since x is a factor of z, if x is even z cannot be odd. (2 is a factor of x when x is even. So 2 must also be a factor of z, since x is a factor of z. This concept will be required later in Stmt II as well)
So that leaves us with two possibilities: (i) x is even, z is even (ii) x is odd, z is even.
Either way, z is even.
SUFF
Stmt II
By the same reasoning above, if y is even, z is also even.
SUFF
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GMAT PREP DS 1
Source: Beat The GMAT — Data Sufficiency |
z/y is integer
that means
1. z is even and y is even
OR z is odd and y is odd
2 y/x is integer
y is even and x is even
OR y is odd and x is odd
3 z/x is integer
z is even and x is even
OR z is odd and x is odd
now
statement I says xz is even
as par 3 z is even Suff
statement II says y is even
as par 1 z is even Suff
that means
1. z is even and y is even
OR z is odd and y is odd
2 y/x is integer
y is even and x is even
OR y is odd and x is odd
3 z/x is integer
z is even and x is even
OR z is odd and x is odd
now
statement I says xz is even
as par 3 z is even Suff
statement II says y is even
as par 1 z is even Suff
