Question

Find the sum of all the natural numbers which are divisible by 4 from 20 to 100.

• A. 1200
• B. 1300
• C. 1240
• D. 1260

Answer 1

The correct option is C 1240

The numbers which are divisible by 4 from 20 to 100 are:
24, 28, 32, 36, ....... 100

Sum of all the natural numbers from 20 to 100 which are divisible by 4
= Sum of natural numbers which are divisble by 4 from 1 to 100 - Sum of integers which are divisble by 4 from 1 to 20
= (4 + 8 + 12 + ... + 100) - (4 + 8 + 12 + 16 + 20)
= 4 (1 + 2 + 3 +....+ 25) - 4 (1 + 2 +....+ 5)

Now, applying the formula of sum of n natural numbers, we get
$4\times \frac{25(25+1)}{2}-4\times \frac{5(5+1)}{2}$
= $(2\times 25\times 26)-(4\times 5\times 3)$
= 1300 - 60
= 1240