List of top Quantitative Aptitude Questions on Linear Inequalities asked in CAT

Find the number of integer pairs (x, y) that satisfy the following system of inequalities:
\[ \begin{cases} x \geq y \geq 3 \\ x + y \leq 14 \end{cases} \]

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

Let $p, q$ and $r$ be three natural numbers such that their sum is 900, and $r$ is a perfect square whose value lies between 150 and 500. If $p$ is not less than $0.3q$ and not more than $0.7q$, then the sum of the maximum and minimum possible values of $p$ is

Find the range of \(x\) satisfying both: \(|2x - 7|<5\) and \(x + 3>0\)

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

The largest real value of a for which the equation\( |x+a|+|x−1|=2\) has an infinite number of solutions for x is

If a and b are non-negative real numbers such that a+2b=6, then the average of the maximum and minimum possible values of (a+b) is