Question

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

• A. 1365
• B. 1256
• C. 1465
• D. 1356

Answer 1

Answer: (D)

${\sum }_{r=2}^{13}\left(7r+2\right)=7.\frac{2+13}{2}\times 6+2\times 12$
$=7\times 90+24=654$
${\sum }_{r=1}^{13}\left(7r+5\right)=7\left(\frac{1+13}{2}\right)\times 13+5\times 13=702$
Total = $654+702=1356$