Trailing Zeros in 100!

CAT 1993 Slot 1 · Quantitative Ability · Medium · QA

This is a medium Quantitative Ability question from the CAT 1993 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

The product of all integers from 11 to 100100 will have the following numbers of zeros at the end.

  1. A.

    20

  2. B.

    24

  3. C.

    19

  4. D.

    22

Answer

B

Explanation

The number of trailing zeros in 100!100! is given by the exponent of 55 in 100!100!: 1005+10025=20+4=24.\left\lfloor \frac{100}{5} \right\rfloor + \left\lfloor \frac{100}{25} \right\rfloor = 20 + 4 = 24.

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