Question

find the sum of all 2 digit numbers which are either multiple of 2 or 3

Answer 1

Heya User,

--> Sum of all 2- digit no.s divisible by 2  :->
       A = 2 ( 1 + 2 + ... + 49 ) = 4900 / 2 = 2450 √√

--> Sum of all 2 - digit no.s divisible by 3 :->
       B = 3 ( 1 + 2 + ... + 33 ) = 1683 √√

--> Now, there are some numbers that are counted in both A and B, which means total such numbers have to be subtracted.

--> Sum of all 2 - digit no.s divisible by both 2 and 3 :->
       C = 6 ( 1 + 2 + ... + 16 ) = 816 √√

=> Sum of all 2 - digit no.s divisible by either 2 or 3 
                                                                  = A + B - C
                                                                  = 2450 + 1683 - 816 
                                                                  =  3317

Hence, the sum of all 2 - digit number divisible by either two or three is 3317 √√