Q5 of 50 Page 21

How many three-digit numbers are there, which leave a remainder 3 on division by 7?

Dividend = (divisor× quotient) + remainder


Here, divisor = 7


Remainder = 3


First 3 digit no. is 100


For, dividend = 100, quotient = 13.6…


Hence, first 3 digit no. divisible by 7 with remainder 3 comes with quotient>13.6… = 14


When quotient = 14, dividend = 101


Last 3 digit no. divisible by 7 with remainder 3 = 997


an = 997


a = 101


d = 7


an = a + (n-1)× d


∴ n-1 = 128


∴ n = 129


Hence,129 numbers are present.


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