Question

Find the
Sum
of
all
numbers
From 100 to 350 which are
which are divisible
(i)divisible by 4 or6 (2)divisible by 4 or 6
(3)Not divisible by 4 nor 6.
(4)Not divisible by 4

Answer 1

Given : Numbers  100 to 350

To Find :  (i)divisible by 4 and 6 (2)divisible by 4 or 6   (3)Not divisible by 4

Solution:

100 to 350

divisible by 4 and 6

if divisible by LCM ( 4, 6)  = 12

108 ,  120 , ........................................................, 348

348 = 108 + (n - 1) 12

=> 240 = (n-1)12

=> 20 = n - 1

=> n = 21

21 numbers are divisible by 4 and 6  from 100 to 350

Sum of numbers  

a = 108

d = 12

n = 21

Sum = (21/2) ( 108 + 348)  = 4788

divisible by 4 or  6

Divisible by 4  + Divisible by 6  - Divisible by 12

Divisible by 4  

100 ,...........................348     => 63 numbers

Divisible by 6  

102 ,...........................348     => 42 numbers

divisible by 4 or  6  = 63 + 42 - 21  = 84  numbers

Sum = (63/2)(100 + 348) + (42/2)(102 + 348)  - 4788

= 14112 + 9450 - 4788

= 18774

Not divisible by 4

Numbers from 100 to 350 = 251

Sum = (251/2)(100 + 350) = 56475

Divisible by 4 = 63    numbers

Not divisible by 4  = 251 -  63

= 192 numbers

Sum =  56475 - 14112   = 42363

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