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

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

1. 1365

2. 1256

3. 1465

4. 1356

Correct Option: , 4

Solution:

$\sum_{r=2}^{13}(7 r+2)=7 . \frac{2+13}{2} \times 6+2 \times 12$

$=7 \times 90+24=654$

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

Total $=654+702=1356$