If x is a positive integer greater than 1…
We are given that x is a positive integer greater than 1 and need to determine the value of x.
Statement One Alone:
2x is a common factor of 18 and 24.
Let’s determine all of the common factors of 18 and 24:
1, 2, 3, and 6.
Since x must be an integer greater than 1, 2x will be an even integer greater than 2. Therefore the only common factor from the above list that can equal 2x is 6. Thus, x = 3. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:
x is a factor of 6.
The factors of 6 are 1, 2, 3, and 6. Since x > 1, x could equal 2, 3 or 6. Since we do not know the exact value of x, statement two is not sufficient to answer the question.