Ans: Let us solve it using the conventional method:
=>a=3 & b=5
a+b=8. Option e.
However, it is advisable to practise questions in more than one method while preparing for any aptitude exam.
From the number 675, we should understand that out of ‘a’ or ‘b’ one must be 5 as LHS is product of two numbers raised to some power. In that case we can reject out options a,b and c as the sum (a+b) definitely would be more than 5. Now we have 2 options left- 7 & 8. If the option d were correct, then the other number would be ‘2’ – in this case the LHS [a6b4]1/2 would definitely have ended in a zero (which is not the case). Thus, “Option e” must be correct.