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.
If x is a 3–digit number, is x even?
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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
- 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
First Statement + Second Statement
- 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.
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
Here we are told that $$a+c=even.$$ This implies that:(1) the sum of the units digit and the hundreds digit is even
- 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
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.(2) the product of all the digits is even
First Statement + Second Statement
Again, we can not conclude anything. We could have:(1) the sum of the units digit and the hundreds digit is even
(2) the product of all the digits is even
- 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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Your Answer
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Global Stats
Target question: Is x even?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
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