Quantitative Ability Question of the Day

A number Y is chosen at random from the set of all prime numbers less than 50. What is the probability that hundred more than one-fifth the square of Y is less than nine times Y?


OPTIONS

1) 0.067
2) 0. 63
3) 0.133
4) 0.5

Solution
Hundred more than one-fifth the square of Y is less than nine times Y.

∴ Y2 – 45Y + 500 < 0.
∴ (Y – 20)(Y – 25) < 0
∴ 20 < Y < 25
Now, there is only one value of Y (Y = 23), which satisfies the given condition.
There are 15 prime numbers less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.

Hence, option 1.