CAT 1993 — QA Question 22

The following Venn diagram shows the distribution of numbers between 1 and 100 that are divisible by 2, 3, 5 or a combination of two or more of them.

Number of numbers divisible by 2 are Quotient of 100/2 = 50
Number of numbers divisible by 3 are Quotient of 100/3 = 33
Number of numbers divisible by 5 are Quotient of 100/5 = 20

Number of numbers divisible by 2 & 5 are Quotient of 100/10 = 10
Number of numbers divisible by 5 & 3 are Quotient of 100/15 = 6
Number of numbers divisible by 3 & 2 are Quotient of 100/6 = 16

Number of numbers divisible by 2, 3 & 5 are Quotient of 100/30 = 3

Total number of numbers that are divisible by one or more among 2, 3 and 5 = 27 + 14 + 7 + 13 + 3 + 7 + 3 = 74.

Hence, the required number = 100 – 74 = 26.

Hence, option (a).