Question Bank • QB_GA_QA_006 MCQ • 1 Mark

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

What is the remainder when $3^{100}$ is divided by 7?

Options:

  • (A) 1
  • (B) 2
  • (C) 4
  • (D) 6

Answer Key:

C

Step-by-Step Solution & Explanation

By Fermat's Little Theorem, since 7 is prime and $\gcd(3, 7) = 1$: $3^{7-1} = 3^6 \equiv 1 \pmod 7$ Express the exponent 100 in terms of multiples of 6: $100 = 6 \times 16 + 4$ Therefore: $3^{100} = (3^6)^{16} \times 3^4 \equiv 1^{16} \times 81 \pmod 7$ $81 = 7 \times 11 + 4 \equiv 4 \pmod 7$ The remainder is 4.
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