IMO D. As it is “could be” question, plugin x=7, only D holds

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If x is a prime number greater than 2, which of the following could be a prime number?

All prime numbers are integers.

The only factors of a prime number are that number and 1.

All prime numbers greater than 2 are odd.

Any even number greater than 2 is not prime.

(A) \(x^2\)

The factors of this number are 1, x, and \(x^2\). So this number cannot be prime.

(B) \(\frac{x}{2}\)

Since all prime numbers greater than 2 are odd, \(\frac{x}{2}\) is not an integer, and therefore will not be prime.

(C) \(3x\)

The factors of this number are 1, 3, x, and 3x. So this number cannot be prime.

(D) \(x - 4\)

An odd prime number minus 4 is an odd number. A odd number could be prime.

Example: 11 - 4 = 7

(E) \(x^2 + 1\)

A prime number greater than 2 is odd. The square of an odd number is an odd number. An odd number + 1 is an even number. An even number greater than 2 is not prime.

The correct answer is (D).
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