Integers: Even and Odd - Definitions

If $$p$$ and $$q$$ are distinct odd prime numbers, which of the following must be true?

Incorrect. [[snippet]] Plug in good numbers such as $$p = 3$$ and $$q= 5$$. In the expression $$3 \cdot 5 = 15$$, which is _not_ a prime number. Therefore, this answer choice is not a "*must* be true" statement. POE and move on.

Incorrect. [[snippet]] Plug in good numbers such as $$p = 3$$ and $$q = 5$$. In the expression $$3+5 = 8$$, which is _not_ a prime number. Therefore, this answer choice is not a "*must* be true" statement. POE and move on.

Incorrect. [[snippet]] Plug in good numbers such as $$p = 3$$ and $$q = 5$$. The answer choice $$\displaystyle \frac{3}{5}$$ is a fraction, which is not prime. Therefore, this answer choice is not a "*must* be true" statement. POE and move on.

Incorrect. [[snippet]] Plug in good numbers such as $$p = 3$$ and $$q = 5$$. In the expression $$3-5 = -2$$, which is _not_ a prime number. Therefore, this answer choice is not a "*must* be true" statement. POE and move on.

Correct. [[snippet]] Plug in good numbers such as $$p= 3$$ and $$q = 5$$. With this plug-in, $$3 + 5 = 8$$ and $$8 \div 2 = 4$$. Clearly 4 is an integer, so this answer choice cannot be eliminated for this plug-in. All other answer choices are eliminated for the same plug-in, so this is the right answer choice.

$$pq$$ is a prime number.

$$p + q$$ is a prime number.

$$\frac{p + q}{2}$$ is an integer.

$$\frac{p}{q}$$ is a prime number.

$$p- q$$ is a prime number.