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How many integers n, 1 <= n <= 4000, are multiples of 16 or 25 or both?

 Jun 2, 2020
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to solve the question, you need to find all the multiples of 16 and 25, and then subtract the overlap.

4000/16 = 250, so there are 250 multiples of 16 that work.

4000/25 = 160, so there are 160 multiples of 25 that work.

The overlap in this question occurs when a number is divisble by both 16 and 25. We counted those overlapping numbers twice so we need to go back and subract them off once.

4000/(16*25) = 4000/400 = 10, so there are 10 overlapping numbers.

The final answer to this problem, therefore, is 250 + 160 - 10 = 400

 

Hope this solutions helps!

 Jun 2, 2020

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