Question

The sum of those integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

• A. 2489
• B. 4735
• C. 2317
• D. 2632

Answer 1

Answer: (D)

First number $=1$
Last number $=100$
Sum of integer 1 to 100
$S=\frac{100}{2}[101]=5050$
numbers which are divisible by 3 are $3,6,\mathrm{9.................99}$
$S_1=\frac{33}{2}[3+99]=33\times 51=1683$
numbers which are divisible by 5 are $5,10\dots \dots \dots .,100$
$S_2=\frac{20}{2}[105]=1050$
numbers which are divisible by 3 and 5 both are $15,30\dots \dots ..90$
$S_3=\frac{6}{2}[15+90]=3(105)=315$
Now sum of integers which are not divisible by 3 or 5
$=S-S_1-S_2+S_3=5050-1683-1050+315=2632$