CAT 2024 Slot 3 QA Q6 Number Systems

Question 6 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

If \(10^{68}\) is divided by 13 , the remainder is
  1. A
    8
  2. B
    9
  3. C
    4
  4. D
    5

Answer: (B) 9 Number Systems MCQ

Solution

  1. \(1001 = 13 \times 77\), so \(10^3 \equiv -1\) and \(10^6 \equiv 1 \pmod{13}\).
  2. \(10^{68} = (10^6)^{11} \cdot 10^2 \equiv 100 \equiv 9 \pmod{13}\).

Same concept in other years

See every question on Remainder of a large power: find the cycle of remainders.

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