Bodhee Prep-CAT Online Preparation

CAT 2019 Quant Question with Solution 54

What is the largest positive integer n such that $\frac{n^{2}+7 n+12}{n^{2}-n-12}$ is also a positive integer?

  1. 8
  2. 12
  3. 16
  4. 6
Show Answer

Correct Answer: Option: 2

$\frac{{{n}^{2}}+7n+12}{{{n}^{2}}-n-12}=\frac{\left( n+3 \right)\left( n+4 \right)}{\left( n-4 \right)\left( n+3 \right)}=\frac{\left( n+4 \right)}{\left( n-4 \right)}$

$\Rightarrow \frac{\left( n+4 \right)}{\left( n-4 \right)}=\frac{\left( n-4+8 \right)}{\left( n-4 \right)}=1+\frac{8}{\left( n-4 \right)}$

The expression is positive integer if $\frac{8}{\left( n-4 \right)}$ is integer.

Or (n-4) must be factor of 8.

For n to be largest, n-4=8

Or n =12

CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1

CAT 2019 Slot-2

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon