If a, b, c, and d are single digit positive integers

If a and b are two-digit positive integers greater than 10, is the remainder when a is divided by 11 less than the remainder when b is divided by 11?

(1) The remainder when a is divided by 69 is the fifth power of a prime number

(2) The remainder when b is divided by 12 is b

Kudos for a correct solution.