This question can be solved with a combination of Exponent Rules and TESTing VALUES.
We're told that B is an INTEGER. We're asked if 2^44 < B^11. This is a YES/NO question.
Fact 1: B is EVEN
B = 0
Then 2^44 is NOT < 0^11 and the answer to the question is NO
B = 10,000,0000
Then 2^44 is < 10,000,000^11 and the answer to the question is YES
Fact 1 is INSUFFICIENT
Fact 2: B is greater than 16
This Fact is more about knowing how to 'rewrite' exponents than anything else.
16^11 can be rewritten as (2^4)^11, which is equal to 2^44.
Since we now know that B is GREATER than 16, B^11 will be GREATER than 2^44. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT
GMAT assassins aren't born, they're made,
EMPOWERgmat GMAT Club Page, Study Plans, & Discounts