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how many numbers between 1 and 500 are divisible by 2 or 3 or 10

how many numbers between 1 and 500 are divisible by 2 or 3 or 10

Grade:12

1 Answers

Arun
25750 Points
6 years ago
Dear students
no divisible by 2 = 500/2 = 250
no divisible by 3 = 500/3 = 166.66 = 166
no divisible by 10 = 500/10 = 50
no divisible by 2 and 3 = n(2 intersection3) = no divisible by 6 = 500/6 = 83.33 = 83
no divisible by 2 and 10 = n(2 intersection10) = no divisible by 20 = 500/20 = 25
no divisible by 2 and 3 = n(3 intersection10) = no divisible by 30 = 500/30 = 16.66 = 16
no divisible by 2 and 3 and 10 = n(2 intersection3 intersection 10) = no divisible by 60 = 500/60 = 8.33 = 8
now n(2 U 3U 10) = n(2) + n (3) + n(10) – n (2 intersection 3) – n(3 intersection 10) – n(2 intersection 10) + n(2 intersection 3 intersection 10)
= 250 + 166+ 50 – 83 – 25 – 16 + 8
= 474 – 124
= 350
Regards
Arun (askIITians forum expert)

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