Is the positive integer P a prime number?
(1) 67 > P > 61
(2) P is even

The answer you have here is wrong, in the explanation you are taking the information from BOTH statements to answer if only statement 1 is sufficient, rather than taking each one separately. So statement 1 by itself is NOT sufficient because it just says that P is between 61 and 67, meaning it could be either 62, 63, 64, 65, or 66 and not all of those are prime.
together ARE sufficient because you could determine that P is not a prime number.

The answer is in fact A. Its a yes or no question. It asks if P can be prime if it is an integer between 61 and 67. The integers in this set are 62, 63, 64, 65, and 66. None of them are prime, so the answer to the question is NO. Therefore, statement one is sufficient.

Statement 2 simply says that P is even. This works if P is 2, but not if its any other even number. And, there is no way to determine which even number P is supposed to be. So, statement two is not sufficient. The answer is A.