If x is a 3–digit number, is x even?

[Gmat_mission]

If x is a 3-digit number, is x even?

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

[spoiler]OA=E[/spoiler].

Why is E the correct answer? Could anyone help me here? Please.

[Vincen]

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.

[Brent@GMATPrepNow]

If x is a 3-digit number, is x even?

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

Target question: Is x even?

Given: x is a 3-digit number,

Jump to......

Statements 1 and 2 combined
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 222. In this case, the answer to the target question is YES, x IS even
Case b: x = 121. In this case, the answer to the target question is NO, x is NOT even
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent