Logical reasoning PrepTest 136 · Section 4 · Question 20

Incorrect. Increase enrollment → not Maintain quality of education. Looking at the chain, this branches off of the premises, so it doesn't build on the chain to justify the conclusion.

Incorrect. Increase enrollment → not Reduce spending next year. This is a negation of the first premise, so it doesn't add to the chain.

Incorrect. Aggressive marketing of programs → Increase enrollment. This is a negation of the premise, so it doesn't add to the chain.

Correct. Argument or Facts:
Argument

Valid or Flawed:
Flawed

Question Type:
Strengthen with Sufficient Premise

Stimulus Summary:
not Increase enrollment → Reduce spending next year
not Aggressive marketing of programs → not Increase enrollment
Therefore - Maintain quality of education → Aggressive marketing of programs

Answer Anticipation:
First, a note on our diagram. We treated "Without" the same way we would "Unless"—as "If not." If you used another method and ended up with the contrapositive of our diagram, there's nothing wrong with that!

Strengthen with Sufficient Premise questions featuring conditional logic are fairly common, and they tend to fall into one of two patterns—either a set of conditionals are provided, and there's a missing connection; or one conditional is provided, and the argument tries to apply it to a specific scenario but fails to establish the sufficient condition is met. This falls into the former camp.

As such, we should get the premises to line up with the conclusion by taking contrapositives to match terms, then combine the premises to see where the gap is. Here, the shared term between the premises and conclusion is about aggressive marketing, which is a positive necessary condition in the conclusion, so we'll need to take the contrapositive of that premise (and the other one to combine them):
not Reduce spending next year → Increase enrollment → Aggressive marketing of programs

From here, we can see that the necessary condition of the conclusion can be justified based on the sufficient condition of not reducing spending next year. However, that's not the connection in the conclusion, so we'll need to connect that term with the one that is included there (or it's contrapositive):
Maintain quality of education → not Reduce spending next year
Reduce spending next year → not Maintain quality of education

Looking at the combined chain above, we can see that adding this to the beginning gives us the conclusion, so let's find it in the answers.

Answer Explanation:
Reduce spending next year → not Maintain quality of education. This answer is the contrapositive of our anticipation, and it builds off of the provided premises to create a chain that represents the conclusion, so this is our answer.

Key Takeaway:
Conditional logic-based Strengthen with Sufficient Premise questions that have multiple conditionals are going to be missing a link in the chain. Get the premises to match up with any term in the conclusion that's shared, then build the chain and see where that missing link is.

Incorrect. Aggressive marketing of programs → not Reduce spending next year. This answer is a reversal of our chain, so it doesn't add anything to the argument that could justify the conclusion.