A politician can neither be reelected nor avoid censure by his or her colleagues if that politician is known to be involved in any serious scandals.
Statements
conditional (if = Left side, sufficient)
if ... then ... politician is known not reelected to be involved in → and any serious scandals will be censured
specific facts
These prominent politicians are involved in a serious scandal. These politicians will not be reelected.
Evaluate
Our reading / thinking goal on Must Be True and Most Supported (i.e. Inference questions) is to see whether we can combine or synthesize any of the claims they've provided in order to derive some other true claim. To do this, we pay attention to whether we're given any Conditional rules, Causal relationships, or Math-y facts. And we pay attention to whether we see any Overlapping Ideas that show up in multiple claims.
The first sentence was conditional, signified by the sufficient indicator "If", so we put the "If" idea on the left of the arrow. When we see "neither Y nor Z", we need to translate this into "not this and not that". People often write "or" because it rhymes with "nor". But the expression neither / nor is banning both things, not one or the other.
That is banning both things, not one or the other.
So "if X, then neither Y nor Z" looks like this: X → ~Y and ~Z
The contrapositive of that rule (reversing the order and the positive/negative value of everything) looks like this (remember that and/or switches when we contrapose): Z or Y → ~X
The first sentence, contraposed, would be saying, If you've been reelected or you never got censured, then you were never known to be involved in any serious scandals.
(you've got to get nostalgic for Test 39's worldview, when being involved in serious scandals had political or electoral consequences)
Since we have a conditional rule, we're looking to see whether any other claims (rules or facts) mention the ideas on the left side or the right side of that rule. The second sentence tells us about politicians who have been involved in a serious scandal.
The rule applies to them! What does the right side tell us about those politicians?
It says, . (Censure = harsh criticism. In the American political system, and others I believe, Impeachment is the most severe rebuke that the political system can give towards its leader. Censure is a non-binding official condemnation. It's like .)
The last sentence tells they will not be reelected. Yeah, last sentence, we know! We're following the rule. We also know that they can't avoid censure.
Goal
Since combining the second sentence with the rule in the first sentence provides us with inferences (these politicians can't be reelected or avoid censure), we have good reason to think the correct answer will just be testing us on these available inferences.
However, because the last sentence stole one of them from us, we'd expect the answer to deal with the other one: these prominent politicians cannot avoid censure (harsh criticism)
But on Must Be True there's no such thing as what the answer should be. We pick whatever answer we can prove from the provided information.