Question: Is x odd?
Statement 1: x/2 is not an integer
Possibilities:
x is odd. For example, x = 3. 3/2 = 1.5, which is not an integer.
x is a fraction. For example, x = 1/2. (1/2)/2 = 1/4, which is not an integer.
Two different possibilities.
Insufficient.
(2) 2x + 3 is odd.
Possibilities:
x is even. For example, x = 2. 2(2) + 3 = 7, which is odd.
x is odd. For example, x = 1. 2(1) + 3 = 5, which is odd.
Two different possibilities.
Insufficient.
Statements Combined:
We have three possibilities from the two statements.
x is odd.
x is even.
x is a fraction.
If we can eliminate two, we will have sufficient information.
If we plug an even number into the expression from Statement 1 we get the following.
Even Number/2 = Integer
This is contrary to Statement 1. So, x cannot be even.
Statement 2 combines 2x + 3 to get an odd number. Since even + odd = odd, 2x must be even.
There is no way to multiply a fraction by 2 to get an even number. Consider the following examples.
2 * 1/2 = 1
2 * 1/3 = 2/3
2 * 1 1/2 = 3
So, x cannot be a fraction.
Therefore, x must be odd.
Sufficient.
The correct answer is C.
