The sum of all the natural numbers from 200 to 600 both inclusive which are neither divisible by 8 n...........

Quantitative Aptitiude (CLAT) Number System

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

1, 23, 968

1, 33, 068

1, 33, 268

1, 87, 332

D(8) = numbers divisible by 8 = 200, 208, 216, 224, 232, 240,………….., 592, 600.

Total D(8) numbers = 51

Sum of D(8) numbers = [(51/2)*(200 + 600)] = (51*400) = 20400

D(12) = numbers divisible by 12 = 204, 216, 228, 240, 252, 264,………….., 588, 600.

Total D(12) numbers = 34

Sum of D(12) numbers = [(34/2)*(204 + 600)] = (17*804) = 13668

Now, D(8 intersect 12) = numbers divisible by both 8 and 12 = 216, 240, 264,…., 576, 600.

Total D(8 intersect 12) numbers = 17

Sum of D(8 intersect 12) numbers = [(17/2)*(216 + 600)] = (17*408) = 6936

So, D(8 union 12) = numbers divisible by either 8 or 12

= D(8) + D(12) - D(8 intersection 12).

So, sum of D(8 union 12) numbers = 20400 + 13668 - 6936 = 27132.

Now, sum of all natural numbers ranging from 200 to 600 = [(401/2)*(200 + 600)] = (401*400) = 160400.

So, sum of all natural numbers from 200 to 600 (both inclusive) which are neither divisible by 8 nor by 12 = (160400 - 27132) = 133268.

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