Explanation

The first two terms in the algebraic expression are both divisible by x^{2}. Once we realize this, the question becomes much simpler: We only need concern ourselves with whether 6x + 9 is divisible by x^{2}.

Statement (1)

Since 4 < x^{2} < 30 and x is prime, we know that x is a prime number greater than 2 and less than or equal to 5. This means x is either 3 or 5. Testing these values in 6x + 9, we find that the expression is divisible for x = 3 but not x = 5. This statement is insufficient.
The answer must be B, C, or E.

Statement (2)

Factoring the quadratic equation gives us (x − 3)(x − 7) = 0, and x = 3 or 7. Both are prime, so both are possible values for x. Testing these values in 6x + 9, we find that the expression is divisible for x = 3 but not x = 7. This statement is not sufficient.

The correct answer is C or E.

Statement (1 & 2)

The only solution for the two statements taken together is x = 3, and the expression in the question stem is divisible by x^{2}.

**The correct answer is C.**

Statement (1)

Since 4 < x

Statement (2)

Factoring the quadratic equation gives us (x − 3)(x − 7) = 0, and x = 3 or 7. Both are prime, so both are possible values for x. Testing these values in 6x + 9, we find that the expression is divisible for x = 3 but not x = 7. This statement is not sufficient.

The correct answer is C or E.

Statement (1 & 2)

The only solution for the two statements taken together is x = 3, and the expression in the question stem is divisible by x

## 2 Comments

Hallo:

I don’t get it.

Statement I gives me one definite solution. (X must be 3, as the term is not devisivle by 5).

Statement II also gives me one definite solution (x must be 3, because the term is not devisible by 7).

Therefore, the correct answer must be D. Each statement allone is sufficient.

Ok, nevermind. I got it