Hello M7MBA.

Let's take a look at this question.

(1) x + y = 12

Since "x" and "y" are prime, then we have two options:

(i) x=5 and y=7.

First, we have to select 5 chairs from 7, this can be done with a combination: $$7C5=\frac{7!}{2!5!}=\frac{7\cdot6\cdot5!}{2\cdot5!}=21.$$ Now, we have to organize the 5 people in the 5 selected chairs, this can be done in 5! different ways. Therefore, the answer to the original question is: $$7C5\cdot5!=21\cdot5!=2520.$$

(ii) x=7 and y=5.

First, we have to select 5 people from 7, this can be done with a combination: $$7C5=\frac{7!}{2!5!}=\frac{7\cdot6\cdot5!}{2\cdot5!}=21.$$ Now, we have to organize the 5 selected people in the 5 chairs, this can be done in 5! different ways. Therefore, the answer to the original question is: $$7C5\cdot5!=21\cdot5!=2520.$$

Since both answers are the same, we can conclude that this statement is SUFFICIENT.

(2) There are more chairs than people.

This doesn't give enough information. Therefore, this statement is NOT SUFFICIENT.

Finally, the correct answer is the option A .

I hope it helps.