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Question
Aman reads 4 newspaper thoroughout the year. He numbered them as 1,2,3.. 365. He reads TOI on days of multiple of 15, HT of 7, IE of 4 and TT of 3 multiple. How many days did he read exactly 2 newspaper and number of days he did not read any newspaper?
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Answer
Number of multiples of 3 = 121, number of multiples of 4 = 91, number of multiples of 7 = 52, number of multiples of 15 = 24.
Number of multiples of LCM of (15,3) = 24,
Number of multiples of LCM of (15,7) = 3,
Number of multiples of LCM of (15,4) = 6,
Number of multiples of LCM of (7,3) = 17,
Number of multiples of LCM of (7,4) = 13,
Number of multiples of LCM of (4,3) = 30,
Number of multiples of LCM of (15,4,3) = 6,
Number of multiples of LCM of (15,3,7) = 3,
Number of multiples of LCM of (15,4,7) = 0,
Number of multiples of LCM of (3,4,7) = 4,
Number of multiples of LCM of (15,3,4,7) = 0
Exactly 2 newspapers = 3+6+24+13+17+30 - (3+4+6) = 93 - 13 = 80
No newspaper = 365-[(121+91+52+24) - 93 + 13] = 365 - 208 = 157
