Q23 - Each new car in the lot at Rollway Motors

[ohthatpatrick]

Question Type:
Match the Reasoning

Stimulus Breakdown:
Conclusion: If a car is between $5-18k, it's a used car that is less than ten years old.
Evidence: If new, then more than $18k. If ten or more years old, then less than $5k.

Answer Anticipation:
The structure here is two conditional premises (with no overlapping ideas). The conclusion says "if the right sides aren't true, then the left sides aren't true", essentially writing a contrapositive that includes the ideas from both conditionals.

P1: A -> B
P2: C -> D
Conc: ~B and ~D -> ~A and ~C

How can we efficiently look for a match? Once we read the two conditional premises, we should think about a trigger would sound like if it were saying, "If NEITHER of these right sides are true".
Correct Answer:
C

Answer Choice Analysis:
(A) The conclusion trigger would need to accomplish "not more than 2" and "not fewer than 2". So the trigger should be "If it has exactly 2". Instead, they have "exactly 2" as the right side of the conclusion.

(B) The conclusion trigger would need to accomplish "not 2 or 3" and "DOES have more than 2". So the trigger would have to be "If it's 4 or more bedrooms". It's not. Eliminate.

(C) YES. The conclusion trigger would need to accomplish "it's fewer than 3" and "2 or more". Since the trigger says "there are exactly 2", this works! Does the right side of the conclusion rule out the two triggers? Yes, because "on the fourth floor" contradicts "above fourth floor" and "below fourth floor".

(D) The conclusion trigger would need to accomplish "more than 2" and "not 3", which basically means "4 or more". Instead, the trigger is about balconies, so eliminate.

(E) The conclusion trigger would need to accomplish "two or fewer" and "vacant", so something like "If a vacant apartment had two or fewer bedrooms". The trigger does NOT match that, so eliminate.

Takeaway/Pattern: This is a tough one. You want to believe you'll be able to use the Conclusion Shortcut and only consider answers whose conclusions have a compound trigger (an "and" in the trigger). But they were clever here and devised mathematical ways of ruling out two ideas with one. Saying "you have exactly 3" rules out "4 our more" and "2 or fewer", for example. This problem certainly would have been wise to skip and come back to.

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