How many numbers from 0 to 999 are not divisible by either 5 or 7?
- A313
- B341
- C686Correct
- D786
Explanation
To find the number of integers from 0 to 999 that are not divisible by 5 or 7, we follow these steps:
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Total numbers: There are 1000 numbers in total from 0 to 999.
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Divisible by 5: These are 0, 5, 10, up to 995. The count is 1000 divided by 5, which is 200.
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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.
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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.
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Divisible by 5 or 7: Using the formula (A + B - Both), we get 200 + 143 - 29 = 314.
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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.
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