CAT 1993 — QA Question 22
Use the following information:
Eighty five children went to an amusement park where they could ride on the merry – go round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re.1, and the total receipt of the amusement park was Rs.145.
The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
Answer & solution
26
- B
18
- C
31
- D
None
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).