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  4. The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is :

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Q. The sum of all two digit positive numbers which when divided by $7 $ yield $2$ or $5$ as remainder is :

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Solution:

$\sum^{13}_{r=2} \left(7r+2\right) = 7. \frac{2+13}{2} \times6 + 2 \times12 $
$ = 7 \times90 +24 = 654 $
$\sum^{13}_{r=1} \left(7r+5\right) = 7 \left(\frac{1+13}{2}\right) \times13+5\times13 = 702 $
Total = $654 + 702 = 1356$