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Question:

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

1365

1256

1356

1465

Solution:

Formula:n∑k=1=12n(n+1)13∑r=2(7r+2)=7⋅2+132×6+2×12=7×90+24=65413∑r=1(7r+5)=7(1+132)×13+5×13=702Total=654+702=1356.