CAT 2024 Number System Question (Medium)

Question

When is divided by 11 , the remainder is

Accepted Answer

Step 1 Find the cyclicity of powers of 3 modulo 11 Compute So, the cycle is 3, 9, 5, 4, 1 quad --- Step 2 Find the exponent position in the cycle Compute 333 div 5 66 3 Thus, corresponds to the 3rd term in the cycle. Cycle 3, 9, 5, 4, 1 The 3rd term is 5 . --- Final Answer 5

CAT 2024

Quantitative

Number System

Medium

When $3^{333}$ is divided by 11 , the remainder is

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