CAT 1991QA Question 32

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.

x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?

Answer & solution

  • (x - 1)yz

  • B

    x(y - 1)z

  • C

    xy(z - 1)

  • D

    x(y + 1)z

Solution

Going by the options:

(a) (x - 1)yz = xyz − yz

(b) x(y - 1)z = xyz - xz

(c) xy(z - 1) = xyz - xy

(d) x(y + 1)z = xyz + xz

Here, yz will be minimum out of yz, xz, xy, xz as x > y > z

Hence, option (a).

CAT 1991 QA Q32: x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product x — Solution | TheCATExam