## How to solve a hard number system question for CAT confidently and quickly 3

Denominator of a fraction is less than the square of the numerator by 1. If 2 is added to both, the fraction will be more than $\frac{1}{3}$. And when 3 is subtracted from both, the fraction remains positive and is smaller than $\frac{1}{10}$. Find the fraction.

For quick solution of this 3rd hard number system question for CAT, explore deeply inequality analysis and inequality algebra...