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)

$1356$

Formula: $\sum _{k=1}^n=\frac{1}{2}n(n+1)$

$\sum _{r=2}^{13}(7r+2)=7\cdot \frac{2+13}{2}\times 6+2\times 12$

$=7\times 90+24=654$

$\sum _{r=1}^{13}(7r+5)=7\left(\frac{1+13}{2}\right)\times 13+5\times 13=702$

Total $=654+702=1356$.