Modular Arithmetic Remainder

CAT 1999 Slot 1 · Quantitative Ability · Easy · Number Systems

This is an easy Quantitative Ability question from the CAT 1999 Slot 1 paper. It tests Number Systems. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

The remainder when 7847^{84} is divided by 342342 is

  1. A.

    0

  2. B.

    1

  3. C.

    49

  4. D.

    341

Answer

B

Explanation

Notice that 73=343=342+17^3 = 343 = 342 + 1. So 784=(73)28=(343)28=(342+1)281281(mod342)7^{84} = (7^3)^{28} = (343)^{28} = (342 + 1)^{28} \equiv 1^{28} \equiv 1 \pmod{342}. The remainder is 11.

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