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The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______.

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Correct answer is 271

D3 = {integers between 1 to 500 divisible by 3}

D5 = {integers between 1 to 500 divisible by 5} 

D7 = {integers between 1 to 500 divisible by 7}

To find number of integers between 1 to 500 that are divisible by 3 or 5 or 7 is to find

= (166 + 100 + 71) - (33 + 23 + 14) + 4

= 337 - 70 + 4 = 271 

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