The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
Explanation:
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).
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