JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Sequences and Series

The two-digit numbers leaving remainder $2$ on division by $7$ run $16,23,\dots ,93$, which is $12$ terms summing to $\frac{12}{2}(16+93)=6\times 109=654$. Those leaving remainder $5$ run $12,19,\dots ,96$, which is $13$ terms summing to $\frac{13}{2}(12+96)=13\times 54=702$. The two families do not overlap, so the total is $654+702=1356$.