i received a pm.

this question is definitely written with an intended answer of (a), and (a) is the best choice.

sharmishtha_goel wrote: A. Mayor Drabble has no political debt that is both of longer standing than the one she owes to Lee and could as suitably be repaid by an appointment to be the new head of the arts commission.

this is the best answer.
the "longer standing" matters because the mayor "always repays debts as soon as possible", implying a rank order of debts based on how long those debts have existed.

think about the negation method here: if this choice is false, then that means that drabble has another debt that (a) has existed for longer AND (b) could just as well be repaid with the appointment. therefore, in that case, drabble would be more likely to give the appointment to that other person, thus destroying the argument.

E. The only way that Mayor Drabble can adequately repay her political debt to Lee is by appointing him to head the arts commission.

the problem here is the word "only".
the argument certainly assumes that the appointment is the BEST way in which drabble could repay the debt, but not necessarily the ONLY way.
the argument is perfectly consistent with the possibility that there are other ways in which drabble could repay the debt, but that those other ways happen to be inferior to this one.

so, if you replace "only" with "best", then this would also be a correct assumption. however, as written, it's wrong.