Question

A natural number is chosen at random from the first 100 natural numbers. Then the probability, for the in-equation $x+\frac{100}{x}>50$ satisfied, is

• A. $\frac{1}{20}$
• B. $\frac{11}{20}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{11}{20}$

$x+\frac{100}{x}>50\Rightarrow x^2-50x+100>0\Rightarrow 1\le x<25-5\sqrt{21},or25+5\sqrt{21}<x\le 100(1\le x\le 100,xϵN)$
$\Rightarrow x=1,2,48,49,50,...,100$
Therefore the total number of ways = 100 and favorable ways = 55
Required probability $=\frac{55}{100}=\frac{11}{20}.$