The correct answer is (C).
Chorus Auditions
Step 1: Overview
Situation: Singers auditioning for a chorus director
Entities: Six singers (Kammer, Lugo, Trillo, Waite, Yoshida, Zinn)
Action: Strict Sequencing. Determine the order in which the singers audition. Even though each singer's audition is recorded or not recorded, there is no Matching component, because it's already announced which singers are recorded and which aren't. If that information were not already concrete, then this would be a Sequencing/Matching Hybrid.
Limitations: The six singers will all be auditioned, and auditions take place one after the other, so this is standard 1:1 Sequencing. It's also noted that two of the singers, Kammer and Lugo, will be recorded while the others will not.
Step 2: Sketch
List the singers by initial and set up a series of six numbered slots. Be sure to distinguish the two singers that are recorded; there are many ways to do so. You can just label the entity list with those that are recorded and those that aren't, you can put the recorded ones in uppercase and the non-recorded ones in lowercase, you can put an "r" under each recorded singer and an "n" under each non-recorded one, etc. It doesn't matter which you choose, just make sure they're at least distinguished in the entity list.
Step 3: Rules
Rule 1 establishes the fourth audition as non-recorded. Depending on your notation, you may consider adding "n" under the fourth slot. You may alternatively or additionally want to put "K" and "L" underneath the slot, which would also capture the rule.
Rule 2 establishes the fifth audition as recorded. Depending on your notation, you may consider adding "r" under the fifth slot. You may alternatively or additionally want to put "K/L" in the slot itself, which would also capture the rule.
Rule 3 requires Waite to audition before both recorded singers (Kammer and Lugo). Kammer and Lugo could still audition in either order. There's no need to necessarily indicate recorded/non-recorded because the sequence already completely represents the rule:
Rule 4 requires Kammer to audition before Trillo. That can be immediately combined with Rule 3.
Rule 5 requires Zinn to audition before Yoshida.
Step 4: Deductions
Most of the deductions come from the orders established in the last three rules. That alone leads to a lot of restrictions about which entities can't be in certain slots. (e.g., per Rule 4, Zinn can't be last and Yoshida can't be first). However, there's one more deduction to consider first. One of the recorded sessions (Kammer or Lugo) will be fifth (Rule 2). The other recorded session cannot be fourth (Rule 1), nor can it be first because Waite must audition beforehand (Rule 3). That means the other recorded session must be second, third, or sixth. However, if it were sixth, that would mean the last two sessions would both be recorded. In that case, it would be impossible for Kammer to audition before Trillo (a non-recorded audition). Therefore, the other recorded session cannot be sixth, so it has to be either second or third. That allows for Limited Options.
If the other recorded session is second, then Waite would have to audition first. Kammer and Lugo would be second and fifth, in either order. Trillo, Yoshida, and Zinn would fill in the remaining spots. Because Zinn has to precede Yoshida (Rule 5), Zinn could not be last and Yoshida could not be third.
If the other recorded session is third, Waite would audition first or second. Kammer and Lugo would be third and fifth, in either order. Trillo would have to audition after Kammer, so Trillo could not be first or second, and thus must be fourth or sixth.
Yoshida has to audition after Zinn, so Yoshida also cannot be first or second—otherwise, it would be in the first two auditions with Waite, leaving no room for Zinn. That would leave Zinn as the only other singer who could audition first or second along with Waite, in either order. That means Trillo and Yoshida would be be fourth or sixth, in either order.
Step 5: Questions
(C) Must Be False (CANNOT Be True)
The correct answer to this question will be someone who cannot be second. The remaining four answers list singers who could.
The second singer could be either recorded singer (Kammer or Lugo), as long as Waite auditions first (as seen in Option I). That eliminates (A) and (B).
If Trillo auditioned second, Kammer would have to audition first (Rule 4). However, that would violate Rule 3 by leaving no space for Waite before Kammer. This is impossible, making (C) the correct answer. For the record:
If the third singer were a recorded singer (Kammer or Lugo), then the first and second singer would be Waite and Zinn, in either order (as seen in Option II). That means either of those singers could be second, which eliminates (D) and (E)
