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Rightmost non-zero digit

CAT 2005 Slot 1 · Quantitative Ability · Medium · Number System

This is a medium Quantitative Ability question from the CAT 2005 Slot 1 paper. It tests Number System. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The rightmost non-zero digit of the number 30272030^{2720} is

  1. A.

    1

  2. B.

    3

  3. C.

    7

  4. D.

    9

Answer

A

Explanation

302720=32720×10272030^{2720} = 3^{2720} \times 10^{2720}. The rightmost non-zero digit is determined by the unit digit of 327203^{2720}. Since 27202720 is divisible by 4, 32720≡34≡1(mod10)3^{2720} \equiv 3^4 \equiv 1 \pmod{10}. Thus, the rightmost non-zero digit is 11.

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