LSAT (Law School Admission Test)Analytical ReasoningHard
A theater group is performing a play with six roles—Lead (L), Support (S), Comic (C), Villain (V), Narrator (N), and Extra (E). Six actors—P, Q, R, T, U, W—are auditioning for these roles. Each actor will be assigned exactly one role, and each role will be filled by exactly one actor. The following conditions apply: * P cannot be assigned the Lead role. * Q must be assigned either the Comic role or the Narrator role. * If R is assigned the Villain role, then W must be assigned the Support role. * U cannot be assigned the Extra role. * T must be assigned the Lead role. If Q is assigned the Comic role, and R is assigned the Villain role, which of the following must be true?
- AP is assigned the Extra role.
- BP is assigned the Narrator role.
- CW is assigned the Extra role.
- DU is assigned the Support role.
Show answer & explanationAnswer & explanation
Correct answer: D. U is assigned the Support role.
Given: T=Lead, Q=Comic, R=Villain. From 'If R is Villain, then W is Support', we get W=Support. Roles filled: L, C, V, S. Actors assigned: T, Q, R, W. Remaining roles: N, E. Remaining actors: P, U. We know U cannot be Extra. Therefore, U must be Narrator, and P must be Extra. This leaves no other option for U.
Why the other options are wrong
- A. P is assigned the Extra role, not Narrator.
- B. P must be Extra, not Narrator, because U cannot be Extra.
- C. W is assigned the Support role, not Extra.
Cascading Deductions
A series of logical inferences where the conclusion of one deduction serves as the premise for the next, leading to a definite outcome.
- Start with fixed assignments.
- Apply conditional rules sequentially.
- Use elimination to narrow down possibilities for remaining elements.
Memory trick: One fact pushes the next, until only one path remains.