Question

The largest negative integer for which$\frac{(x-4)(x-2)}{(x-1)(x-5)}>0$ is

• A. -2
• B. -1
• C. -3
• D. -4

Answer 1

The correct option is B -1

$\frac{(x-4)(x-2)}{(x-1)\cdot (x-5)}>0$

$\Rightarrow$ either$(x-4)(x-2)>0and(x-1)(x-5)>0$

or $(x-4)(x-2)<0and(x-1)(x-5)<0$

$\Rightarrow$ either $x\in (-\infty ,2)\cup (4,\infty )$

$x\in (-\infty ,1)\cup (5,\infty )$

or $x\in (2,4)andx\in (1,5)$

$\Rightarrow$ largest -ve integer is

$-1$