Question

$\text{Find the sum of integers from 1 to 100 which are divisible by 2 or 5.}$
[4 marks]

Answer 1

$\text{Integers divisible by}2\text{(Up to 100)}=2,4,6,\cdots ,98,100$
[0.5 mark]
$\text{Integers divisible by}5\text{(Up to 100)}=5,10,15,\cdots ,95,100$
[0.5 mark]
$\text{Let,}{S}_1=\text{Sum of numbers divisible by 2(Up to 100)}{S}_2=\text{Sum of numbers divisible by 5(Up to 100)}{S}_3=\text{Sum of numbers divisible by 10(Up to 100)}\Rightarrow \text{Sum of number divisible by 2 or 5(Up to 100)}=S_1+S_2-S_3\cdots \left(i\right)$
[1 mark]
$\text{Let's first find}{S}_1,S_1=2+4+6+\cdots +98+100S_1=2(1+2+3+\cdots +49+50)S_1=\frac{2\times 50\times (50+1)}{2}=2550$
[0.5 mark]
$\text{Similarly,}{S}_2=\frac{5\times 20\times (20+1)}{2}=1050\text{and}{S}_3=\frac{10\times 10\times (10+1)}{2}=550$
[1 mark]
$\text{Now, After putting these values in (i),}\text{Sum of number divisible by 2 or 5(Up to 100)}=2550+1050-550=3050$
[0.5 mark]