An experiment consists of eight steps - H, J, K, L, M, O, P, and S - that all must be performed. Three days are allotted for the experiment. Each step requires exactly one morning or else one afternoon to be performed, and at most two steps can be performed during any given morning or afternoon. The following restrictions must be observed: J must be performed on the second day. P must be performed in the morning. K and M must be performed at the same time. J must be performed at some time after M has been completed and at some time after O has been completed. O must be completed at some time before P and at some time before S. If J is performed in the morning, which of the following must be performed on the first day?
A. H
B. K
C. L
D. P
E. S
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Explanation: Total 8 steps, 3 days, max 2 steps per slot (Morning/Afternoon). J must be on Day 2. K and M must be simultaneous (2 slots). M and O must be before J. If J is Day 2 Morning (1 slot), then the tasks before J (M and O) must be completed before Day 2 Morning. The earliest time for M and O to be completed is Day 1. Since K and M must be simultaneous (2 slots) and must be done by Day 1, and O must also be done by Day 1 (1 slot). This means K, M, and O (3 steps, 3 slots) must be done on Day 1. The remaining 5 steps (H, L, P, S, 1 more slot) must be done in the remaining 3 slots on Day 1 (1 slot) and Day 2 (3 slots). The minimum 3 tasks (K, M, O) **must** be done on Day 1. The remaining Day 1 slot must be filled by H, L, P, or S. The question asks what **must** be performed on the first day. The required steps (K, M, O) before J must be done on Day 1. Since K is an option and K is part of the mandatory group (K, M, O) on Day 1, K **must** be performed on the first day.
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