Here's a more formal approach.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.
Target question: Is z even?
Given: x is a factor of y, and y is a factor of z.
There's a nice rule that says, "If D is a factor (divisor) of N, then N = kD for some integer k"
So, if x is a factor of y, then y = kx for some integer k.
Also, if y is a factor of z, then z = jy for some integer j
Statement 1: xz is even
This sets up two possible cases (x is even or z is even). We'll examine both:
case a: x is even.
If x is even, then kx is even, which means y is even (since y=kx).
If y is even, then jy is even, which means z is even (since z=jy).
case b: z is even
Since both possible cases yield the same answer to the target question, statement 1 is SUFFICIENT
Statement 2: y is even
If y is even, then jy is even, which means z is even (since z=jy).
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
