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Problem 5 - Entrance Test

What is the remainder when 3^101 is divided by 5?

Correct: D

We look for a pattern in the remainders when powers of 3 are divided by 5: 3^1 % 5 = 3, 3^2 % 5 = 4, 3^3 % 5 = 2, 3^4 % 5 = 1, 3^5 % 5 = 3. The remainders repeat in a cycle of length 4: 3, 4, 2, 1. Since 101 = 4 * 25 + 1, the remainder when 3^101 is divided by 5 is the same as the remainder when 3^1 is divided by 5, which is 3.