CAT 1991QA Question 33

Number TheoryEasy
Passage / Data

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as  well as a library was one fourth the number of those having a laboratory alone. The number of schools  having either a laboratory or a library or both was 35.

What is the greatest power of 5 which can divide 80! exactly.

Answer & solution

  • A

    16

  • B

    20

  • 19

  • D

    None of these

Solution

Number of powers of 5 in 80! = (805=16) + (165=3) = 19.

Hence, option (c).

CAT 1991 QA Q33: What is the greatest power of 5 which can divide 80! exactly. — Solution | TheCATExam