Mathematics - Sets and Relations Question with Solution | TestHub

Here $B=\left\{2,4,6,8....,200\right\}$

Sum of elements in $A\cap B$

$=\underset{\mathrm{Multiple} \mathrm{of} 2}{\underbrace{\left(2+4+6+\dots +200\right)}}-\underset{\mathrm{Multiple} \mathrm{of} 2 \& 3 \mathrm{i}.\mathrm{e}. 6}{\underbrace{\left(6+12+\dots +198\right)}}$

$-\underset{\mathrm{Multiple} \mathrm{of} 5 \& 2 \mathrm{i}.\mathrm{e}. 10}{\underbrace{\left(10+20+\dots +200\right)}}+\underset{\mathrm{Multiple} \mathrm{of} 2,5 \& 3 \mathrm{i}.\mathrm{e}. 30}{\underbrace{\left(30+60+\dots +180\right)}}$

$=2\left(\frac{100\times 101}{2}\right)-6\left(\frac{33\times 34}{2}\right)-10\left(\frac{20\times 21}{2}\right)+30\left(\frac{6\times 7}{2}\right)$

$=5264$