What is the sum of all two digit numbers which when divided by 3 leaves 2 as the remainder ?
(a)1565
(b)1585
(c)1635
(d)1655

Options

A. 1565
B. 1585
C. 1635
D. 1655

Answer

C

Explanation

The numbers which divided by 3, leaving remainder 2 will be of form `3x+2`
Given, `3x+2` is 2-digit number
So, x can be from 3 to 32
Sum of numbers `=underset(x=3)overset(32)sum(3x+2)`
`=3(3+4+5+...+32)+(2+2+......)" "...(i)`
`3,4,5...32" is an A.P with "a=3,d=1,T_(n)=32`
`:.T_(n)=a+(n-1)1`
`impliesn-1=29impliesn=30" terms"`
`:.(1)implies3(3+4+5+...+32)+(2+2...30" times")`
`=3((30)/(2)(3+32))+(2xx30)(becauseS_(n)=(n)/(2)(a+l))`
`=(90)/(2)(35)+60`
`=(45xx35)+60`
`=1575+60=1635`