Find the maximum value of $a*b$?
(1) $a$ and $b$ are prime numbers
(2) $a+b = 10$

I initially thought (1) alone might work because primes, but then I realized we don't know if a and b are positive or if order matters. Also, primes can be negative? Usually in GMAT, prime numbers are positive integers greater than 1. So a and b are at least 2. But still, without a sum constraint, product can be huge. So (1) not enough.

For (2), a+b=10. To maximize ab, we want a and b as close as possible. The max product for real numbers is 25, but since they don't have to be integers? Wait, are a and b integers? The problem doesn't specify. If they can be any real numbers, then max is 25, but if integers, then 5*5=25, but 5 is not prime. So combined with (1), a and b must be prime and sum to 10. Possible prime pairs: (3,7) and (7,3) both give 21, and (5,5) but 5 is prime, sum 10, product 25. Actually 5 is prime! So 5 and 5 are prime and sum to 10. So product 25. So both together give 25. But wait, is 5 considered prime? Yes. So both sufficient.

I think the answer is C. Statement 1 gives primes, statement 2 gives sum 10. Together, possible pairs: (3,7) product 21, (5,5) product 25, (7,3) product 21. So max is 25. So both needed.