GMAT, GRE [ Remainders ]

${}^{}$What is the remainder when 11^12 is divided by 12 ?





Let's look at the cycle of remainders: 

What is the remainder of 7 divided by 4? Ans = 3
What is the remainder of 6 divided by 4? Ans = 2
What is the remainder of 5 divided by 4? Ans = 1
What is the remainder of 4 divided by 4? Ans = 0
What is the remainder of 3 divided by 4? Ans = -1

(11^1)/12 gives a remainder of 11 or -1

(Remainder of 11/12)^12gives us (-1)^12
which is 1