Explanation

The sum 100 is even, so one of the three primes must be 2 (an odd+odd+odd sum is odd). The other two sum to 98 and differ by 36: solving p+q = 98, p−q = 36 gives 67 and 31, both prime. The triple is {2, 31, 67}; none of 17, 29, 43 occurs, so the answer is 'None of the above'.