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If x is a 3–digit number, is x even?

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Source: — Data Sufficiency |
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by Vincen » Mon Jun 18, 2018 2:47 am

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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.
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by Brent@GMATPrepNow » Mon Jun 18, 2018 4:47 am

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Gmat_mission wrote: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
Brent Hanneson - Creator of GMATPrepNow.com
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