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
Answers
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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