CAT 1991 — QA Question 41

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 = $\frac{(25y^2+75y)}{3}=\frac{25y(y+3)}{3}$

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).