CAT 2025 Slot 1 QA Question 4: The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x y \geq 3$ and $x + y

Question

The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x > y \geq 3$ and $x + y < 14$ is

Accepted Answer

We count the possible values of x for each possible integer value of y.
For $y = 3$, $x$ can be 4, 5, 6, 7, 8, 9 or 10. This gives 7 pairs.
For $y = 4$, $x$ can be 5, 6, 7, 8 or 9. This gives 5 pairs.
For $y = 5$, $x$ can be 6, 7 or 8. This gives 3 pairs.
For $y = 6$, $x$ can only be 7. This gives 1

The number of distinct pairs of integers (x,y)(x, y)(x,y) satisfying the inequalities x>y≥3x > y \geq 3x>y≥3 and x+y<14x + y < 14x+y<14 is

The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x > y \geq 3$ and $x + y < 14$ is