UPSC Prelims 2026 CSAT, question 42

Solution.

Answer: (c) 8

1. Any positive integer power of $6$ ends in $6$, so the units digit of $6^{129}$ is $6$.
2. The units digits of powers of $7$ repeat in a cycle of $4$ ($7, 9, 3, 1$); since $307 = 4 \times 76 + 3$, the units digit of $7^{307}$ is $3$.
3. Therefore, the units digit of $6^{129} \times 7^{307}$ is the units digit of $6 \times 3 = 18$, which is $8$.