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

Question

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

Dr. Abubacker · Accepted Answer

(c)
$x + \frac{100}{x} > 50$
$\Rightarrow x^{2} + 100 > 50\ x\ \ \ (\because x \in N)$
$\Rightarrow x^{2} - 50x + 100 > 0$
$\Rightarrow (x - 25)^{2} > 525$
$\Rightarrow x - 25 < - \sqrt{525}\ or\ x - 25 > \sqrt{525}$
$\Rightarrow x < 25 - 22.9\ or\ x > 25 + 22.9$
$\Rightarrow x \leq 2\ or\ x \geq 48$
Hence, the number of favourable cases = 2+ 53 = 55
Thus, required probability $= \frac{55}{100} = \frac{11}{20}$

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

Explanation

Reviewed by Dr. Abubacker

Want more practice?