UPSC Prelims 2010·GS1·science-and-technology·science and technology

How many numbers from 0 to 999 are not divisible by either 5 or 7?

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Last updated 23 May 2026, 3:31 pm IST
  1. A313
  2. B341
  3. C686Correct
  4. D786

Explanation

To find the number of integers from 0 to 999 that are not divisible by 5 or 7, we follow these steps: 1. Total numbers: There are 1000 numbers in total from 0 to 999. 2. Divisible by 5: These are 0, 5, 10, up to 995. The count is 1000 divided by 5, which is 200. 3. Divisible by 7: These are 0, 7, 14, up to 994. Since 994 divided by 7 is 142, and including 0, there are 143 numbers. 4. Divisible by both 5 and 7 (divisible by 35): These are 0, 35, 70, up to 980. Since 980 divided by 35 is 28, and including 0, there are 29 numbers. 5. Divisible by 5 or 7: Using the formula (A + B - Both), we get 200 + 143 - 29 = 314. 6. Not divisible by either: Subtract the result from the total count. 1000 - 314 = 686. Therefore, 686 numbers are not divisible by either 5 or 7. Correct option is C.
science-and-technology: How many numbers from 0 to 999 are not divisible by either 5 or 7?

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