The positive integers x, y and z are such that x is a factor of y and y is a factor of z. Is z even.
1) xz is even
2) y is even.
Let's reverse the language:
z is a multiple of y, and y is a multiple of x.
Thus, z is a multiple of x.
Statement 1: xz is even.
If x = even, then z must be even since it's a multiple of an even value.
If x = odd, then z must be even in order for xz to be even.
Since in either case z is even, sufficient.
Statement 2: y is even.
If z is a multiple of an even number, then z too must be even.
Sufficient.
The correct answer is
D.
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