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The numbers between 1 and 2011 are written on a piece of paper. Logan circles the even numbers with red
circles and Miranda circles the multiples of 5 with blue circles. How many numbers are circled with only one
color?

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The numbers between 1 and 2011 are written on a piece of paper. Logan circles the even numbers with red
circles and Miranda circles the multiples of 5 with blue circles. How many numbers are circled with only one
color?

Answer:

Numbers between 1 and 2011 => 2, 3, ..., 2010.

Even numbers : 2, 4, 6, 8, ..., 2010 => 1005 numbers.

Numbers multiple of 5 : 5, 10, 15, ..., 2010 => 402 numbers.

Numbers of double count : even + multiple of 5 : 10, 20, ..., 2010 => 201.

Numbers are circled with only one color => 1005 + 402 - 201 = 1206.

 Mar 4, 2021

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