CAT 2021 Set-1 | Quantitative Aptitude | Question: 8

Question

$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if

• A. $ – 2 < x < 3 \; \text{or} \; x > 9 $
• B. $ x < – 5 \; \text{or} \; 3 < x < 9 $
• C. $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $
• D. $ x < – 5 \; \text{or} \; – 2 < x < 3 $

Answer 1

Given that, $f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$

Now, if $f(x) < 0$

Then, $\dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18} < 0$

$ \Rightarrow \dfrac{x^{2} + 5x – 3x – 15}{x^{2} – 9x + 2x – 18} < 0$

$ \Rightarrow \dfrac{(x+5)(x-3)}{(x-9)(x+2)} < 0$

We can draw the number line.



$x \in (-5, -2) \cup (3, 9)$

$ \boxed{-5 < x < -2 \; \text{(or)} \; 3 < x < 9}$

Correct Answer $:\text{C}$

Comments

I think the explanation given to the answer is incorrect. Please correct me if I am wrong