CAT 1991 — QA Question 41
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.
In Sivakasi, each boy’s quota of match sticks to fill into boxes is not more than 200 per session. If he reduces the number of sticks per box by 25, he can fill 3 more boxes with the total number of sticks assigned to him. Which of the following is the possible number of sticks assigned to each boy?
Answer & solution
- A
200
150
- C
125
- D
175
Let x be the total number of sticks assigned to each boy and y be the number of boxes in which he has to fill them. If he reduces number of sticks per box by 25, he would fill (x/y - 25) in each box and hence he would now fill (y + 3) boxes.
∴ x = (x/y - 25)(y + 3) = x + 3x/y - 25y - 75.
⇒ 3x = (25y + 75)y
⇒ x =
For x to have an integer value, y(y + 3) has to be a multiple of 3. This is possible only when y is a multiple of 3.
Subsequently, (y + 3) will be a multiple of 3.
Therefore, 25y(y + 3)/3 = x will be a multiple of 3.
Hence, option (b).