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

Explanation

All these number will be of the form 8k+2 or 8k+5
Sum of all 2 digit nos. which leaves 2 as remained = `sum_(k=1)^(12) (8k + 2) = (8 xx 12 xx 13)/(2) + 2 xx 12 = 648`
Sum of number of the form 8k + 5 `= sum_(k=1)^(11) (8k + 5) = (8 xx 11 xx 12)/(2) + 5 xx 11 = 583`
Total sum = 648 + 583 + 1231