What is the remainder if 2^192 is divided by 6?

1. B. 1
2. C. 2
3. D. 4

Answer: D

Explanation

To find the remainder when 2^192 is divided by 6, we can observe the pattern of remainders of powers of 2 when divided by 6:
2^1 = 2 (Remainder 2)
2^2 = 4 (Remainder 4)
2^3 = 8 (Remainder 2)
2^4 = 16 (Remainder 4)
The pattern of remainders is 2, 4, 2, 4… We observe that if the power of 2 is odd, the remainder is 2; if the power of 2 is even (and greater than or equal to 2), the remainder is 4. Since the power 192 is an even number, the remainder when 2^192 is divided by 6 will be 4. This question tests number theory concepts, specifically remainders and cyclicity, which are common in CSAT.