How many positive integers not exceeding 2001 are multiples of 3 or 4 but not 5 ?

Explanation

Number of multiples of 3 till 2001=`[2001/3]=667`..(1)

number of multiples of 4 till 2001=`[2001/4]=500`..(2)

Number of multiple of 3 and 4(`3xx4=12`)=`[2001/12]=166`...(3)

Number of multiples of 15 ( multiples of 3 and 5)=`[2001/15]=133`...(4)

Number of multiples of 20 ( multiples of 4 and 5)=`[2001/20]=100`...(5)

Number of multiples of 60 ( multiples of 3,4 and 5)=`[2001/60]=83`...(6)

Answer=>`667+500-166-133-100+83=801`

`[ x ]` represents greatest integer function

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