A cloud server processes data batches across three sequential stages (k = 1, 2, 3). At the… — GMAT

A cloud server processes data batches across three sequential stages ( $k = 1, 2, 3$ ). At the start ( $k = 0$ ), the server has a Buffer size of $B_0 = 100\text{ MB}$ and a Queue size of $Q_0 = 50\text{ MB}$ . In each stage $k$ , the sizes are updated according to the following rules:
- $B_k = B_{k-1} - 20\text{ MB}$
- $Q_k = Q_{k-1} + 10\text{ MB}$

Which of the following statements about the state of the server are true?

At the end of Stage 2 ( $k = 2$ ), the Buffer size $B_2$ is $60\text{ MB}$ .Cevap
At the end of Stage 3 ( $k = 3$ ), the Queue size $Q_3$ is $80\text{ MB}$ .Cevap
C
At the end of Stage 3 ( $k = 3$ ), the Buffer size $B_3$ is $60\text{ MB}$ .
D
At the end of Stage 2 ( $k = 2$ ), the Queue size $Q_2$ is $60\text{ MB}$ .
E
At the end of Stage 1 ( $k = 1$ ), the combined total volume $B_1 + Q_1$ is $150\text{ MB}$ .

Cevap

The correct statements are that at the end of Stage 2, the Buffer size is

60\text{ MB}

, and at the end of Stage 3, the Queue size is

80\text{ MB}

The correct statements accurately reflect the iterative evaluation of the state transition formulas: the buffer size decreases by

20\text{ MB}

each stage to reach

60\text{ MB}

at Stage 2, and the queue size increases by

10\text{ MB}

each stage to reach

80\text{ MB}

at Stage 3.

Adım Adım Çözüm

Calculate state values at Stage 1 (

k = 1

)

B_1 = 100 - 20 = 80\text{ MB}

and

Q_1 = 50 + 10 = 60\text{ MB}

. Combined total:

140\text{ MB}

Apply the given state transition rules to the initial values at

k = 0

Calculate state values at Stage 2 (

k = 2

)

B_2 = 80 - 20 = 60\text{ MB}

and

Q_2 = 60 + 10 = 70\text{ MB}

Apply the transition rules to the Stage 1 state values.

Calculate state values at Stage 3 (

k = 3

)

B_3 = 60 - 20 = 40\text{ MB}

and

Q_3 = 70 + 10 = 80\text{ MB}

Apply the transition rules to the Stage 2 state values.

Evaluate option statements

The statement specifying

B_2 = 60\text{ MB}

and the statement specifying

Q_3 = 80\text{ MB}

are verified as correct.

Compare calculated stage states directly against the option statements.

Anahtar Kavram

Sequential processes require evaluating every state transition iteratively without skipping intermediate stages.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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