Question

The sum of the integers from $1$ to $100$ which are divisible by $3$ and $5$, is :

• A. $2317$
• B. $2632$
• C. $315$
• D. $2489$

Answer 1

The correct option is C $315$

Integers divisible by $3$ are $\{3,6,9,12,15,.....99\}$

Integers divisible by $5$ are $\{5,10,15,25,30,.....95,100\}$

Set of integers which are divisible by both $3$ and $5$ is the intersection of above sets and that is

$\{15,30,45,....,90\}$ i.e. multiples of $15$ upto $100$

$\therefore$ Sum of the integers which are divisible both $3$ and $5$
$=15+30+45+...+90$
$=\frac{6}{2}(15+90)$..(as there are six such numbers)
$=315$