NinetynineCAT 2025 Slot 3 QA Q13 Inequalities & Modulus
Question 13 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.
In a school with 1500 students, each student chooses any one of the streams out of science, arts, and commerce, by paying a fee of Rs 1100, Rs 1000, and Rs 800, respectively. The total fee paid by all the students is Rs 15,50,000. If the number of science students is not more than the number of arts students, then the maximum possible number of science students in the school is
TITA: type in the answer. There are no options and no negative marking.
Answer: 700 Inequalities & Modulus TITA
Solution
- \(s + a + c = 1500\) and \(1100s + 1000a + 800c = 15{,}50{,}000\).
- Subtract \(800 \times\) the first: \(300s + 200a = 3{,}50{,}000 \Rightarrow 3s + 2a = 3500\).
- With \(a \ge s\): \(3500 = 3s + 2a \ge 5s \Rightarrow s \le 700\).
- \(s = a = 700\), \(c = 100\) works, so the maximum is 700.