Question
Download Solution PDFHow many numbers are there from 500 to 650 (including both) which are divisible neither by 3 nor by 7?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The numbers are from 500 to 650 which are divisible neither by 3 nor by 7
Calculation:
The total numbers up to 500 are divisible by 3 = 500/3 → 166 (Quotient)
The total numbers up to 500 are divisible by 7 = 500/7 → 71 (Quotient)
The total numbers up to 500 are divisible by 21 = 500/21 → 23 (Quotient)
The total numbers up to 650 are divisible by 3 = 650/3 → 216 (Quotient)
The total numbers up to 650 are divisible by 7 = 650/7 → 92 (Quotient)
The total numbers up to 650 are divisible by 21 = 650/21 → 30 (Quotient)
⇒ The total number divisible by 3 between 500 and 650 = 216 - 166 = 50
⇒ The total number divisible by 7 between 500 and 650 = 92 - 71 = 21
⇒ The total number divisible by 21 between 500 and 650 = 30 - 23 = 7
The total numbers from 500 to 650 = 150 + 1 = 151
∴ The required numbers = 151 - (50 + 21 - 7) = 151 - 64 = 87
∴ The are total 87 numbers from 500 to 650 (including both) which are neither divisible by 3 nor by 7
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