Logical reasoning PrepTest 133 · Section 2 · Question 20

Incorrect. The argument already established that if Herbert had been the murderer, he would have left foot/fingerprints that the police would have found. Additionally, this doesn't address the assumption in the argument that no one besides Herbert and Samantha was at the office that day.

Incorrect. The argument establishes that being in Jansen's office the day of the murder is necessary for someone to be the murderer. As such, it doesn't matter where the murder happened, as that relationship holds no matter where the crime occurred.

Correct. Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Strengthen with Sufficient Premise

Stimulus Summary:
Jansen's murdered → In office day of murder
Sam and Herbert - In office day of murder
Herbert the murderer → Police found his fingerprints or footprints at crime scene
Samantha the murderer → She wouldn't have left finger/footprints at crime scene
Police - Found fingerprints but no footprints. The fingerprints weren't Herbert's.
Therefore - Herbert isn't the murderer, and
Therefore - Samantha is the murderer

Answer Anticipation:
This argument follows a common method of reasoning—ruling out alternatives. The argument concludes that Samantha is the murderer, but it doesn't provide any positive proof of her guilt. Instead, it rules out Herbert as the murdered.

When an argument proceeds by ruling out alternatives, it must do two things. First, it must establish that the list of possibilities it establishes is exhaustive—it includes all possibilities. Second, it has to effectively rule out all alternatives.

Let's look at each of these in order.

First, did the argument effectively establish that Herbert and Samantha are the only possible murderers? It did not. While the murderer must have been in the office the day of the murder, and Samantha and Herbert were there, the argument doesn't establish that they were the only ones there. If other people were there, as well, then it's possible that they're the murderer. The argument assumes no one else was present, and therefore couldn't be the murderer, so this will need to be established in the correct answer.

Second, ignoring that first flaw, did the argument effectively rule out the other potential option it raises? Yep. If Herbert were the murderer, then the cops would have found his finger/footprints at the crime scene. They didn't, so he's definitely not the murderer.

So the flaw in this argument is that it fails to establish that Samantha and Herbert are the only two who could have committed the murder (or that they were the only two at the office the day of the murder), and so the correct answer will state this.

Answer Explanation:
Being in the office the day of the murder is a requirement for being the murderer. If Samantha and Herbert were the only two there that day, then one of them must be the murderer, and since the premises establish it couldn't have been Herbert, it must have been Samantha. This answer validates the conclusion, so it's the correct answer.

Key Takeaway:
Common argument structures and reasoning types have elements that need to show up in them for the conclusion to be valid. For example, here, an argument that rules out alternatives needs to establish that the list of alternatives is complete and the other alternatives are all effectively eliminated. Knowing these elements can help you identify which element is missing and thus what the assumption of the argument is.

Incorrect. The argument doesn't establish anything about the connection between the fingerprints and the guilty party, so this answer is out of scope.

Incorrect. While this answer is necessary for the argument to work (the contrapositive of the rule about Samantha's prints tells us that if she left behind finger/footprints, she's not the murderer), it's not sufficient to draw the conclusion. Her fingerprints not being at the scene doesn't guarantee she committed the crime—just that she might have.