CAT 2025 Slot 1 QA Q14 Number Systems

Question 14 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was

TITA: type in the answer. There are no options and no negative marking.

Answer: 55 Number Systems TITA

Solution

Let there be \(b\) boys and \(g\) girls. For \(40\%\) and \(60\%\) to be whole numbers, \(b\) and \(g\) are multiples of 5.
Remaining: \(0.6g = 0.4b + 8 \Rightarrow 3g = 2b + 40\).
With \(b > 10\): \(b = 15\) gives \(3g = 70\) (no) and \(b = 20\) gives \(3g = 80\) (no); \(b = 25\) gives \(g = 30\).
Minimum total \(= 25 + 30 = 55\).