Question

The sum of all the natural numbers from 200 to 600 (both inclusive) which are neither divisible by 8 nor by 12 is:

Options

• 1, 23, 968

• 1, 33, 068

• 1, 33, 268

• 1, 87, 332

Answer 1

1, 33, 268

Explanation:

Sum of no. from 200 to 600

a = 200, d = 1, n = 600 - 200 + 1 = 401

`"S"_401=401/2[200+600]`....{`"S"_"n"="n"/2("a"+"l")`}

`=401/2(800)=401xx400`

⇒ 160400

Sum of numbers divisible by both 8 or 12

= n (8) + n (12) − n (LCM of 8 and 12)

Sum of numbers divisible by 8

`=51/2[200+600]=51xx400=20400`

Sum of numbers divisible by 12

`=34/2(204+600)=17xx804=13668`

Sum of numbers divisible by 24  .....(LCM of 8 and 12)

`=17/2(216+600)=17xx408=6936`

Sum of numbers divisible by 8 or 12

= 20400 + 13668 − 6936 = 27132

Sum of numbers neither divisible by 8 nor 12

= 160400 − 27132 = 133268