Please note that 44's largest divisor is 44, not 22 as you stated. So, 44 can't be used as a proof for S1 insufficiency.
How many divisors does positive integer N has got
1)The difference between the largest and the smallest divisor of N is 21
2) N+1 has 2 divisors
OA is A.
Take statement 1, smalles divisor of any number is 1, largest divisor is 22 if the difference is 21.
Take N = 44, it has got 1,2,4,11 and 22, now take 22, it has got 1,2,11 & 22. so A is not sufficient
Take statement 2, N+1 has 2 divisors, meaning N+1 is a prime number hence not sufficient
combining A & B also is not sufficient, hence correct choice is E.
Please advise with explanation