Presumably when they wrote PQ, they meant the product of P and Q and not that PQ was a two digit number.
Statement 1 tells you that PQ has to equal 1 more than a power of 2. We know from the original info that PQ is less than 70. Let's start with that. This means PQ could equal 3, 5, 9, 17, 33, 65
You also know from the original info though that PQ has to be the product of 2 distinct prime numbers. This eliminates 3, 5, 9, and 17 from the list as there is no way to multiply two prime numbers together to yield those numbers. It however leaves 33 (3 x 11) and 65 (5 x 13). Since two answers remain, statement 1 is insufficient.
Statement 2 yields a multitude of possibilities (again assuming the problem originally stated or should have stated "the product of P and Q). For example we already have 65 from statement 1 as well as 21 for example (3 x 7). 21 would be the product of two primes as well as the sum would add up to 3, a prime number. Therefore, statement two is insufficient.
Taken together however, statement 1 left us with only 33 and 65, and since 33 adds up to 6 it violates statement 2, but 65 adds up to 11, a prime number, 65 is the only number that fits both statements. This means taken together (answer choice C) the statements are sufficient.
