How many numbers are there from 500 to 650 (including both) which are neither divisible by 3 nor by 7?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 87
Total numbers up to 500 are divisible by 3 = 500/3 = 166
Total numbers up to 500 are divisible by 7 = 500/7 = 71
Total numbers up to 500 are divisible by 21 = 500/21 = 23
Total numbers up to 650 are divisible by 3 = 650/3 = 216
Total numbers up to 650 are divisible by 7 = 650/7 = 92
Total numbers up to 650 are divisible by 21 = 650/21 = 30
Total number divisible by 3 between 500 and 650 = 216 - 166 = 50
Total number divisible by 7 between 500 and 650 = 92 - 71 = 21
Total number divisible by 21 between 500 and 650 = 30 - 23 = 7
Total numbers from 500 to 650 = 150 + 1 = 151
The required numbers = 151 - (50 + 21 - 7) = 151 - 64 = 87