sparkles3144 wrote:Is X an odd integer?

A. X^2 is an odd integer
B. 2x is an even integer

The answer is A.

I am not sure if it is A.

Can't I take x=(3)^1/2 and x = 3?
In that case, X does not have to be an integer.

If this is the correct wording of the question then you're right - the answer is not A.

Knowing that x^2 is an odd integer does not ensure that x itself is odd.
As you state, x could equal sqrt(3) in which case x^2 is odd, but x is not odd
Or x could equal 5 in which case x^2 is odd, and x is odd

What's the source of this question?

Cheers,
Brent

sparkles3144 wrote:Is x an odd integer?

1) x² is an odd integer
2) 2x is an even integer

Here's one solution . . .

Target question: Is x an odd integer?

Statement 1: x² is an odd integer
There are several values of x that meet this condition. Here are two:
Case a: x = 5 (5² = 25, and 25 is odd). In this case x is an odd integer
Case b: x = √3 ((√3)² = 3, and 3 is odd). In this case x is not an odd integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2x is an even integer
There are several values of x that meet this condition. Here are two:
Case a: x = 1, in which case x is an odd integer
Case b: x = 2, in which case x is not an odd integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that there are 2 possibilities for the value of x
Possibility #1: x is an odd integer
Possibility #2: x is the square root of an odd integer, where x itself is not an integer

From statement 2, we can be certain that x is an integer. We know this because we cannot multiply a non-integer by 2 and get an even integer as the product.
So, we can rule out Possibility #2, leaving us with Possibility #1, which means x must be an odd integer.

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent