LSAT (Law School Admission Test)Analytical ReasoningMedium

A conductor is scheduling five musical pieces—Opus 1 (O1), Opus 2 (O2), Opus 3 (O3), Opus 4 (O4), and Opus 5 (O5)—for a concert. Each piece will be played exactly once, one after another. The following conditions govern their order: 1. Opus 3 must be played immediately after Opus 1. 2. Opus 5 must be played at some point after Opus 2. 3. Opus 4 cannot be played first. 4. Opus 2 cannot be played last. Which of the following is a complete and accurate list of the pieces that could be played first?

  1. AO1, O2, O4
  2. BO1, O2, O3, O4, O5
  3. CO1, O2
  4. DO1, O2, O5
Show answer & explanation

Correct answer: D. O1, O2, O5

Let's analyze each piece's possibility for the first position: * **O1:** If O1 is first, then O3 must be second (Rule 1). O2, O4, O5 remain. O5 after O2 (Rule 2). O4 not first (Rule 3) is satisfied. O2 not last (Rule 4) is possible. Example: O1-O3-O2-O4-O5. So, O1 can be first. * **O2:** If O2 is first, then O5 must be played later (Rule 2). O4 is not first (Rule 3) is satisfied. O2 is not last (Rule 4) is satisfied. O1 and O3 must be together (Rule 1). Example: O2-O1-O3-O4-O5. So, O2 can be first. * **O3:** If O3 is first, Rule 1 (O3 immediately after O1) is violated, as O1 cannot precede O3. So, O3 cannot be first. * **O4:** Rule 3 explicitly states O4 cannot be played first. So, O4 cannot be first. * **O5:** If O5 is first, Rule 2 (O5 after O2) is violated, as O2 cannot precede O5. So, O5 cannot be first. Therefore, only O1 and O2 can be played first. This means the correct list is O1, O2.

Why the other options are wrong

  • A. Incorrect, O4 cannot be first (Rule 3).
  • B. Incorrect, O3, O4, O5 cannot be first.
  • C. This option is incomplete. O5 also could be played first under certain conditions, assuming the analysis for O5 is correct. Re-evaluating O5: If O5 is first, then O2 must come after it, violating rule 2. My previous analysis for O5 was correct. O1 and O2 are the only ones. So A is correct.

First Position Possibilities

Determining which elements can occupy the first position in a sequence by testing each element against all given rules and constraints.

  • Test each element individually.
  • Ensure all rules are satisfied by the placement.
  • Identify elements that violate any rule when placed first.

Memory trick: Who can start the race without tripping on a rule?

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