A natural number is chosen at random from the first 100 natural numbers. The probability that `x+(100)/x > 50` is `1//10` b. `11//50` c. `11//20` d. none of these

Options

A. `1//10`
B. `11/50`
C. `11/20`
D. none of these

Answer

C

Explanation

We have,
`x + (100)/(x) gt 50`
or `x^(2) + 100 gt 50x`
or `(x - 25)^(2) gt 525`
`implies x - 25 lt - sqrt(525) or x - 25 sqrt(525)`
`implies x lt 25 - sqrt(525) or x gt 25 + sqrt(525)`
As x is a positive integer and `sqrt(525)` = 22.91, we must have `x le 2` or `x ge 48`. Thus, the favorable number of cases is 2 + 53 = 55. Hence, the required probability is `55//100` = `11//20`.