QJEEM19Ma7267: JEE Main 2019 Mathematics - Class 11 JEEM19Ma7267 Solution: The sum of all two digit positive numbers which when divided by …

Question

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

Accepted Answer

\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 (\frac{1 + 13}{2}) \times 13 + 5 \times 13 = 702

Total = 654 + 702 = 1356

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