A natural number is chosen at random from the first 100 natural numbers.

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

Options:

A . 120

B . 1120

C . 13

D . 14

Answer: Option B
:
B

x + \frac{100}{x} > 50 \Rightarrow x^{2} - 50 x + 100 > 0 \Rightarrow 1 \leq x < 25 - 5 \sqrt{21}, o r 25 + 5 \sqrt{21} < x \leq 100 (1 \leq x \leq 100, x ϵ N)

\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} .

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