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How many three-digit numbers are multiples of neither 5 nor 7?

 Dec 2, 2018
 #1
avatar+17332 
+3

NOT positive about this....

100 thru 999 is 900 3-digit numbers

 

there are 180 multiples of 5

there are 128 multiples of 7

there are 26 multiples of 35  (which must be subtraced to avoid double counting)

 

900 - (180+128-26) = 618       Corrected after input from Rom....Thanx ! 

 Dec 2, 2018
edited by ElectricPavlov  Dec 2, 2018
 #2
avatar+4471 
+2

I'm showing 128 multiples of 7

 

618 total

Rom  Dec 2, 2018
 #3
avatar+3994 
+2

Good job, EP! I'll just go over the formula. These steps are called PRINCIPLE OF INCLUSION AND EXCLUSION, and it comes up in many problems. Just what EP said, overcounts are there, and you have to remove them!

 Dec 2, 2018

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