Question

number of positive integers not exceeding 2021 that are multiple of 3 and 4 but not of 5 is equal to

Answer 1

Number of multiples of 3 till 2001=[20013]=667..(1)

number of multiples of 4 till 2001=[20014]=500..(2)

Number of multiple of 3 and 4(3×4=12)=[200112]=166...(3)

Number of multiples of 15 ( multiples of 3 and 5)=[200115]=133...(4)

Number of multiples of 20 ( multiples of 4 and 5)=[200120]=100...(5)

Number of multiples of 60 ( multiples of 3,4 and 5)=[200160]=83...(6)

Answer=>667+500−166−133−100+83=801

[x] represents greatest integer function

(1) and(2) were added and (3) was subtracted because it is not written "3 and 4." (4) and(5) are also subtracted because these numbers are multiples of 5 also.(6) is added because the numbers in (4) and (5) overlapped and were deducted twice.

801 is the required answer