sparkles3144 wrote:Is the integer x even?

(1) x^2 is an even integer.

(2) x/4 is an odd integer.

For (1) can I safely assume that x has to be an integer?

Can't x be (2)^(1/2)?

Yes, you can assume that x is an integer. It says so in the question ("...integer x ...")

Target question: Is the integer x even?

Statement 1: x^2 is an even integer.
If (x)(x) is even, then it must be the case that x is even

To demonstrate this, consider the following rules:
(odd)(odd) = odd
(odd)(even) = even
(even)(even) = even
So, if the product of two integers is even, then it must be the case that either both numbers are even or one is odd and one is even.
Since, x^2 requires us to multiply x by itself, we can rule out the possibility of one number being odd and the other number being even. This means that both numbers (x and x) are even.

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x/4 is an odd integer.
We need only focus on the part that says, x/4 is an integer.
Let's say that x/4 = k (where k is an integer)
This means that x = 4k
In other words, x = (2)(2)k, which means x is a multiple of 2, which means x is definitely even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

sparkles3144 wrote: Can't I assume that x can be square root of 2?

The question tells us that x is an integer.
The square root of 2 is approximately 1.4
Since 1.4 is not an integer, x cannot equal sqrt(2).

sparkles3144 wrote: Do I need to assume that x is an integer?

It's not an assumption. You are explicitly told that x is an integer.

Cheers,
Brent

sparkles3144 wrote:Hello Brent,

I understand all this.

I just wanted to know about (1).

Can't I assume that x can be square root of 2?
square of (2)^1/2 is 2.
Then, x does not have to be even integer.

Do I need to assume that x is an integer?

Consider this analogous question:
X is a female tennis player. Who is X?
(1) X won the 2013 Wimbleton Singles title
(2) blah blah blah

Aside: There are two singles titles: one for the winning male and one for the winning female.
In 2013, Andy Murray won the men's title, and Marion Bartoli won the women's title.

So, is statement 1 sufficient?
Well, we cannot say that person X is either Andy Murray or Marion Bartoli, because Andy Murray is not a woman.
So, statement 1 is SUFFICIENT.

Cheers,
Brent