Question

Consider a set a = {1, 2, 3, .., 1000}. How many members of a shall be divisible by 3 or by 5 or by both 3 and 5 ?

Answer 1

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Answer 2

Given : Set A={1, 2, 3, .., 1000}

Number divisible by 3 from set A

999 is the last number that is divisible by 3 in set A.

$999=333\times 3$

333 numbers in set A divisible by 3.

Number divisible by 5 from set A

1000 is the last number that is divisible by 5 in set A.

$1000=200\times 5$

200 numbers in set A divisible by 5.

The number that is divisible by 3 and 5 should be divisible by 15.

$990=66\times1 5$

66 numbers in set A divisible by both 3 or 5.

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