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Question

Difficulty: MediumSorting and Multi-Column Ordering

The table below presents operational metrics for seven regional grain storage elevators.

Elevator IDRegionStorage Capacity (thousand metric tons)Annual Throughput Rate (%)Average Loading Time (hours)
AlphaMidwest52082%3.2
BetaPlains52078%4.1
GammaMidwest60085%2.8
DeltaDelta45091%3.5
EpsilonPlains45088%2.9
ZetaMidwest60074%3.1
EtaDelta38095%2.4

If the table is sorted in descending order by Storage Capacity (thousand metric tons), and ties are broken by sorting in ascending order by Average Loading Time (hours), which elevator occupies the 4th position from the top?

  1. A
    Alpha
  2. BetaAnswer
  3. C
    Delta
  4. D
    Gamma
  5. E
    Zeta

Answer

Elevator Beta occupies the 4th position from the top after primary sorting descending by Storage Capacity and secondary sorting ascending by Average Loading Time.
Sorting the table primarily by Storage Capacity in descending order places the two elevators with 600 thousand metric tons (Gamma and Zeta) at the top, occupying positions 1 and 2. The next highest capacity tier is 520 thousand metric tons, shared by Alpha and Beta. Applying the secondary sort rule (Average Loading Time in ascending order), Alpha has a shorter loading time (3.2 hours3.2\text{ hours}) than Beta (4.1 hours4.1\text{ hours}). Thus, Alpha takes the 3rd position and Beta takes the 4th position.

Step-by-Step Solution

1
Group facilities by the primary column: Storage Capacity (thousand metric tons) in descending order.
Group 1 (600 thousand metric tons): Gamma, Zeta; Group 2 (520 thousand metric tons): Alpha, Beta; Group 3 (450 thousand metric tons): Delta, Epsilon; Group 4 (380 thousand metric tons): Eta.
Primary sort priority dictates ordering largest values to smallest values first.
2
Apply the tie-breaker criterion (Average Loading Time in ascending order) to Group 1 (Capacity = 600).
Gamma (2.8 hours) comes before Zeta (3.1 hours). Positions 1 and 2 are Gamma and Zeta.
Shorter loading times rank higher in ascending order.
3
Apply the tie-breaker criterion (Average Loading Time in ascending order) to Group 2 (Capacity = 520).
Alpha (3.2 hours) comes before Beta (4.1 hours). Position 3 is Alpha, and Position 4 is Beta.
Since 3.2<4.13.2 < 4.1, Alpha takes the 3rd spot and Beta takes the 4th spot.

Key Concept

Multi-Column Table Sorting and Secondary Tie-Breaking Logic

Alternative Method

Filter out the lower capacity groups (450 and 380 thousand metric tons) immediately since the top 4 spots must belong to the highest capacity groups (600 and 520). Compare only Alpha and Beta for the 4th spot by looking at their loading times.
Estimated Time:1m 30s
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Topics

Sorting and Multi-Column Ordering

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