Hello Gmat_mission.

Let's see your question.

We know that x is a 3-digit number. So, x=abc.

Now, we want to know if c is even or not.

First Statement

(1) the sum of the units digit and the hundreds digit is even

Here we are told that $$a+c=even.$$ This implies that:

- a and c are both even.
- a and c are both odd.

Since we got two different options for c, this statement is not sufficient.

Second Statement

(2) the product of all the digits is even

Now, we are told that $$a\cdot b\cdot c=even$$ This implies that one of the digits is even. Since we could have that c is even or not, Then this statement is not sufficient.

First Statement + Second Statement

(1) the sum of the units digit and the hundreds digit is even
(2) the product of all the digits is even

Again, we can not conclude anything. We could have:

- 323.
- 224.

So, using both statements together is not sufficient.

This implies that the correct answer is the option E.

I hope it is clear enough.