Question

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

• A. 3000
• B. 3050
• C. 4050
• D. 5000

Answer 1

The correct option is B 3050

Set of numbers divisible by $2$ are $2,4,6,...,100$

Set of numbers divisible by $5$ are $5,10,15,...,100$

Set of numbers divisible by $10$ are $10,20,30,...,100$

Now, sum of numbers divisible by $2$ are given by

$S_2=\frac{50}{2}\{2+100\}=25\left\{102\right\}=2550$

Sum of numbers divisible by $5$ are given by

$S_5=\frac{20}{2}(5+100)=10\left(105\right)=1050$

Sum of numbers divisible by $10$ are given by

$S_{10}=\frac{10}{2}(10+100)=5\left(110\right)=550$

Hence required sum $=S_2+S_5-S_{10}=2550+1050-550=3050$