Question

A natural number $x$ is chosen at random from the first $100$ natural numbers. The probability that $x+\frac{100}{x}>50$ is

• A. $1/10$
• B. $11/50$
• C. $11/20$
• D. None of these

Answer 1

The correct option is D None of these

$x+\frac{100}{x}>50$
$x^2-50+100>0\iff (x-25{)}^2>525$
$\iff x-25<-\sqrt{525}$ or $x-25>\sqrt{525}$
$\iff x=1,2$ or $x\ge 48$
$\therefore n\left(E\right)=2+53=55$ and $n\left(S\right)=100$
Hence required probability $\frac{n\left(E\right)}{n\left(S\right)}=\frac{55}{100}=\frac{11}{20}$