JEE MAIN - Mathematics (2019 - 10th January Morning Slot - No. 12)
The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -
1356
1256
1365
1465
Explanation
$$\sum\limits_{r = 2}^{13} {(7r + 2) = 7.{{2 + 13} \over 2}} \times 6 + 2 \times 12$$
= 7 $$ \times $$90 + 24 = 654
$$\sum\limits_{r = 1}^{13} {(7r + 5) = 7\left( {{{1 + 13} \over 2}} \right)} \times 13 + 5 \times 13 = 702$$
Total = 654 + 702 = 1356
= 7 $$ \times $$90 + 24 = 654
$$\sum\limits_{r = 1}^{13} {(7r + 5) = 7\left( {{{1 + 13} \over 2}} \right)} \times 13 + 5 \times 13 = 702$$
Total = 654 + 702 = 1356
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