Question

The sum of integers from 1 to 100 which are divisible by 2 or 5 is-

• A. 300
• B. 3050
• C. 3200
• D. 3250

Answer 1

Answer: (B)

3050

L.C.M. of 2 and 5 is 10.
Numbers divisible by 10 will contain numbers which are also divisible by 2 and 5. . Thus the number divisible by 10 will occur twice. Hence we can write $S=S_2+S_5-S_{10}$
Now, $S_2=\frac{\mathrm{2.50.51}}{2}=2550$ by $\sum n=\frac{n(n+1)}{2}$
Similarly, $S_5=1050,S_{10}=550$
$\therefore S=S_2+S_5-S_{10}$
$=2550+1050-550=3050$