If x is a positive integer greater than 1

jjjinapinch wrote:If x is a positive integer greater than 1, what is the value of x?
(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

Official Guide question
Answer: A

Target question: What is the value of x?

Given: x is a positive integer greater than 1

Statement 1: 2x is a common factor of 18 and 24
Positive factors of 18: 1, 2, 3, 6, 9, 18
Positive factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
COMMON factors of 18 and 24: 1, 2, 3, 6
So, 2x = 1, 2x = 2, 2x = 3 or 2x = 6
This means, x = 0.5, x = 1, x = 1.5 or x = 3
Since we're told that x is a positive integer greater than 1, we can see that x MUST equal 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is a factor of 6
So, x could equal 1, 2, 3, or 6
Since we're told that x is a positive integer greater than 1, we can see that x COULD equal 2, 3, or 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

jjjinapinch wrote:If x is a positive integer greater than 1, what is the value of x?
(1) 2x is a common factor of 18 and 24
(2) x is a factor of 6

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.

Answer: A