Sufficient & Necessary Questions Question 39

If there are any inspired performances in the concert, the audience will be treated to a good show. But there will n...

JennaArthur on September 21, 2019

Why is the answer A?

I diagrammed this question using the transitive property: Inspired performance -> Good Show -> Sophisticated Learners -> Understand Musical Roots. I graphed the answer choice A as: SL -> Inspired Musical Performance Would this not be going backwards since the arrow is a "one way street?"

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Skylar on September 21, 2019

@Kaitlyn,

Your diagram and use of the transitive property is correct is correct. We have: IP -> GS -> SL -> UMR.

To get the contrapositive of this transitive statement, we must both reverse and negate it. Therefore, the contrapositive is: not UMR -> not SL -> not GS -> not IP.

Answer choice A is diagrammed as: not SL -> not IP.
This is where you seem to have gotten confused and overlooked the word "no" before both variables. A states "IF there are no sophisticated listeners," "THEN there will be no inspired musical performances." Remember, "if" introduces Sufficient while "then" introduces Necessary, so this becomes: no sophisticated listeners -> no inspired performances.

Answer choice A is consistent with our contrapositive, so it is correct. Be cautious of the other answer choices that do not follow the correct order of variables.

Does this make sense? Please let us know if you have any other questions!

zingerspecial on September 13, 2021

this response was helpful, thanks