Question

Find the sum of all even positive and integers less than $200$ which are not divisible by $6$.

• A. $6535$
• B. $6539$
• C. $6534$
• D. $6532$

Answer 1

Answer: (C)

$6534$

Sum of even the integers less than $200$ and which are not divided by $6$.

$S_1=2+4+6+\mathrm{8....}+198$

$S_2=6+12+\mathrm{36...198}$

_____________________

$S_1-S_2=2(1+2+\mathrm{3....99})-6(1+2+....33)$

$=2\left(\frac{99\times 100}{2}\right)-6\left(\frac{33\times 34}{2}\right)$ [$\because$ sum of first 'n' natural numbers $=\frac{n(n+1)}{2}$]

$=9900-3(33\times 34)$

$=9900-3366$

$\Rightarrow 9900-3366$

$\therefore S_1-S_2=6534$.