Guideline: Support It is improper for public officials to influence the award of contracts or to perform other acts related to their office in a way that benefits themselves. ████ ███ ██████████ ██ ████ ███████████ ██████ ██ ████████
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The author concludes that the mayor acted improperly. She builds her argument on two premises:
(1) If a public official uses their position to benefit themselves, it is improper.
(2) The mayor used her position to benefit a relative. 
The author attempts to trigger the conditional in premise (1) using premise (2), but the author is assuming that using one’s office to benefit a relative also benefits oneself. We need a rule linking these two ideas, which gives us the following prediction:
If one uses their office to benefit a relative, this benefits oneself.
Which one of the following ██████████ ████ █████ ██ ██████████ ███ ███████████ ██ ███ ██████████
Public officials, when ██████████ █████ ███████ ██████ ██ ████ ██ ██████ █████████ ████ ███████ ████████████
(A) is irrelevant to the conclusion. This would prove that the mayor should be held to a higher standard than a citizen, but this does not prove that they acted improperly.
Publicly funded contracts ██████ ██ ███████ █████ █████████ ██ ████ ███ ███ ███████████ ██ ███ ███████████
Wrong trigger. The premises tell us nothing about the cost and reliability of the mayor’s relative’s services. They could very well have met these qualifications, so (B) doesn’t help us prove the mayor did anything wrong.
Creating the appearance ██ ███████████ ██ ██ ███████████ ██ ██████ ███████████
Irrelevant. The premises never tell us whether the mayor appeared to act improperly. And even if they did, we are trying to prove that the mayor was improper, not that they are to blame for anything.
Awarding a contract ██ █ ███████████ ████████ ████████ ██████ ██ ████████ ██ ██████ █████████ █████
(D) proves the wrong conclusion. We want to prove that the mayor acted improperly, not that they took an excessive risk.
Benefiting one's family ██ ███████ ██████ ██ ████████ ██ ██████████ ████████
The mayor benefited her relative by using her office. (E) tells us this is the same as benefiting oneself, and the premises tell us that benefiting oneself using one’s office is improper. As such, the mayor behaved improperly, and the conclusion is properly drawn.