Explanation

(d)
Let $S = 1 + 2 + 3 + ... + 100$
$= \frac{100}{2}(1 + 100) = 50(101) = 5050$
Let $S_{1} = 3 + 6 + 9 + 12 + ... + 99$
$= 3(1 + 2 + 3 + 4 + ... + 33)$
$= 3.\frac{33}{2}(1 + 33) = 99 \times 17 = 1683$
Let $S_{2} = 5 + 10 + 15 + ... + 100$
$= 5(1 + 2 + 3 + ... + 20)$
$= 5.\frac{20}{2}(1 + 20) = 50 \times 21 = 1050$
Let $S_{3} = 15 + 30 + 45 + ... + 90$
$= 15(1 + 2 + 3 + ... + 6)$
$= 15.\frac{6}{2}(1 + 6) = 45 \times 7 = 315$
$\therefore\$Required sum $= S - S_{1} - S_{2} + S_{3}$
$= 5050 - 1683 - 1050 + 315 = 2632$