SOLUTION: How many integers, 1 to 1000, inclusive, are divisible by neither 2 nor 5?

Question 251902: How many integers, 1 to 1000, inclusive, are divisible by neither 2 nor 5?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Even numbers are divisible by 2, odd numbers are not. Of the numbers 1 to 1000, half of them are odd, so half of them are not divisible by 2.

Numbers that end in either 5 or 0 are divisible by 5. Of the 500 odd numbers in the range 1 to 1000, none of them end in 0 because any number that ends in 0 is even. All 500 of those odd numbers end in 1, 3, 5, 7, or 9, evenly distributed, so one-fifth of them end in 5.

That means that 4/5 of the 500 odd numbers is not divisible by either 2 or 5.

John

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