LSAT (Law School Admission Test)Analytical ReasoningHard
A university committee is composed of exactly five members selected from a pool of eight candidates: three professors (R, S, T) and five students (U, V, W, X, Y). The selection of members must conform to the following conditions: 1. The committee must include at least two professors. 2. If Professor R is selected, then Student U must also be selected. 3. Student V and Student W cannot both be selected. 4. If Student X is selected, then Professor T cannot be selected. 5. If Student Y is selected, then Student U cannot be selected. If Professor S is NOT selected for the committee, which of the following must be true?
- AStudent V is selected.
- BStudent X is selected.
- CProfessor T is selected.
- DStudent U is selected.
Show answer & explanationAnswer & explanation
Correct answer: C. Professor T is selected.
If Professor S is not selected, and there are only two other professors (R, T), then to meet the 'at least two professors' rule (rule 1), both Professor R and Professor T must be selected. So, Professor T must be selected.
Why the other options are wrong
- A. V does not have to be selected. W could be selected instead, provided V is not, and other rules are met.
- B. If X is selected, T cannot be selected (rule 4). But we already deduced that T *must* be selected. Therefore, X *cannot* be selected, making this option false.
- D. If R is selected (which it must be), then U must be selected (rule 2). However, Y could also be selected, which would mean U cannot be selected (rule 5). This creates a contradiction unless Y is not selected. So U doesn't *have* to be selected (if Y is also not selected, U could be selected, or not, depending on other choices).
Must Be True Inference
A conclusion that is logically necessitated by the given rules and a specific premise, regardless of other variable choices.
- Often derived by combining multiple rules.
- Represents an unavoidable outcome.
- Can lead to the elimination of other possibilities.
Memory trick: Premise Sparks Sure Conclusions.