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Difficulty: MediumSequential Processes and State Transitions

An automated data processing node manages a queue of records across three sequential processing stages (k=1,2,3k = 1, 2, 3). The initial batch size at stage k=0k = 0 is N0=400N_0 = 400 records. In each stage kk, the batch size undergoes two consecutive transitions:
1. The batch size is reduced by 50%50\% due to quality filtering.
2. Exactly 120120 newly verified records are added to the batch.

Which of the following statements regarding the batch size across these stages are correct? Select all that apply.

  1. The batch size at the end of Stage 1 (N1N_1) is 320320 records.Answer
  2. The batch size at the end of Stage 3 (N3N_3) is 260260 records.Answer
  3. The total net reduction in batch size from the start of Stage 1 to the end of Stage 3 is 140140 records.Answer
  4. D
    The batch size at the end of Stage 2 (N2N_2) is 160160 records.
  5. E
    Immediately after the filtering reduction step in Stage 1, the batch size is 320320 records.

Answer

The correct statements are: the batch size at the end of Stage 1 is 320 records; the batch size at the end of Stage 3 is 260 records; and the total net reduction from Stage 1 to Stage 3 is 140 records.
Evaluating each stage sequentially shows: Stage 1 ends with 320 records (400 halved to 200, plus 120); Stage 2 ends with 280 records (320 halved to 160, plus 120); Stage 3 ends with 260 records (280 halved to 140, plus 120). Subtracting the final count of 260 from the initial count of 400 gives a net decrease of 140 records.

Step-by-Step Solution

1
Calculate state transitions for Stage 1 (k=1k = 1).
Initial N0=400N_0 = 400. Filtering reduces count to 400×0.5=200400 \times 0.5 = 200. Adding 120 records gives N1=200+120=320N_1 = 200 + 120 = 320.
Tracking each sub-step sequentially is necessary to determine the state at the end of Stage 1.
2
Calculate state transitions for Stage 2 (k=2k = 2).
Filtering reduces count to 320×0.5=160320 \times 0.5 = 160. Adding 120 records gives N2=160+120=280N_2 = 160 + 120 = 280.
Stage 2 operates on the output state of Stage 1 (N1=320N_1 = 320).
3
Calculate state transitions for Stage 3 (k=3k = 3).
Filtering reduces count to 280×0.5=140280 \times 0.5 = 140. Adding 120 records gives N3=140+120=260N_3 = 140 + 120 = 260.
Stage 3 operates on the output state of Stage 2 (N2=280N_2 = 280).
4
Evaluate the net overall change from start to end.
Net reduction = N0−N3=400−260=140N_0 - N_3 = 400 - 260 = 140 records.
Comparing initial state N0N_0 and final state N3N_3 gives the overall change.

Key Concept

Sequential state transitions require updating the system state step-by-step without omitting intermediate additions or reductions.
Estimated Time:1m 30s
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Topics

Sequential Processes and State Transitions

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