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Q58 (CISF/2024) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Which one among the following digits can never be at the units place in (273)n, where n is a positive integer?

Result
Your answer: —  ·  Correct: C

Explanation

The units digit of any power (273)n is determined solely by the units digit of the base, which is 3. To find the possible units digits, we observe the cyclicity of the powers of 3:

  • 31 = 3
  • 32 = 9
  • 33 = 27 (units digit is 7)
  • 34 = 81 (units digit is 1)
  • 35 = 243 (units digit is 3)

The units digits follow a repeating pattern or cycle: {3, 9, 7, 1}. This means that for any positive integer n, the units digit of (273)n must be one of these four numbers. Comparing this cycle to the given options, we see that 1, 3, and 7 are all possible units digits. However, 5 is not part of the cycle and therefore can never appear at the units place.

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