CAT 1991QA Question 35

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.

Find the minimum integral value of n such that the division 55n/124 leaves no remainder.

Answer & solution

  • 124

  • B

    123

  • C

    31

  • D

    62

Solution

As 55 does not have factor common with 124, for 55n to be exactly divisible by 124, n should be a multiple of 124.

Hence the minimum value that n can have is 124 itself.

Hence, option (a).

CAT 1991 QA Q35: Find the minimum integral value of n such that the division 55n/124 leaves no remainder. — Solution | TheCATExam