GATE 2016 EE (EE2) – Question 10

The units digit of $211^{870}+146^{127}\times3^{424}$ is ________.

Show answer and explanation

Correct answer: 7.0 to 7.0

Explanation

Only base units digits matter. 211 ends in 1, so every positive power ends in 1. Likewise 146 ends in 6 and every positive power ends in 6.

Powers of 3 repeat 3,9,7,1 with period four. Since 424 is divisible by four, 3^424 ends in 1. The total therefore ends in 1+6×1=**7**.

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