Probability - Quant/Math - CAT 2013

Question 4 the day: August 06, 2002
The question for the day is from the topic Probability.

What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?

(1)

2 / 15

(2)

4 / 15

(3)

1 / 15

(4)

4 / 90

Solution:

There are a total of 90 two digit numbers. Every third number will be divisible by '3'. Therefore, there are 30 of those numbers that are divisible by '3'.

Of these 30 numbers, the numbers that are divisible by '5' are those that are multiples of '15'. i.e. numbers that are divisible by both '3' and '5'. There are 6 such numbers -- 15, 30, 45, 60, 75 and 90.

We need to find out numbers that are divisible by '3' and not by '5', which will be 30 - 6 = 24.

24 out of the 90 numbers are divisible by '3' and not by '5'.

The required probability is therefore,

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