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Difficulty: MediumCaselets and Paragraph-Based Data

A metropolitan public library system launched a project to digitize a total of 12,00012,000 rare manuscripts. The manuscripts were distributed among three main facilities: the Central Library, the North Branch, and the South Branch in the ratio of 5:4:35:4:3, respectively. After one month of continuous operations, a progress report revealed that the Central Library had successfully digitized 60%60\% of its allocated manuscripts. The North Branch had completed 45%45\% of its assigned quota, while the South Branch managed to digitize 70%70\% of the manuscripts allocated to it.

Based on the information provided in the passage, which of the following statements are correct? (Select all that apply)

  1. The North Branch currently has a greater number of manuscripts left to digitize compared to the Central Library.Answer
  2. The three facilities combined successfully digitized a total of 6,9006,900 manuscripts during the first month.Answer
  3. C
    The South Branch accounted for exactly 70%70\% of the total manuscripts digitized across all three facilities combined.
  4. D
    The Central Library digitized 1,2001,200 fewer manuscripts than the North Branch during the first month.

Answer

The correct statements are that the North Branch has more manuscripts left to digitize than the Central Library, and that the three facilities combined digitized a total of 6,900 manuscripts.
Based on the data derived from the caselet, the three facilities digitized a total of 3,000+1,800+2,100=6,9003,000 + 1,800 + 2,100 = 6,900 manuscripts. Additionally, the North Branch has 2,2002,200 manuscripts remaining (4,000−1,8004,000 - 1,800), which is strictly greater than the Central Library's 2,0002,000 remaining manuscripts (5,000−3,0005,000 - 3,000).

Step-by-Step Solution

1
Calculate the initial allocation of manuscripts for each facility based on the 5:4:35:4:3 ratio.
Central Library: 5,0005,000; North Branch: 4,0004,000; South Branch: 3,0003,000.
The total ratio parts are 5+4+3=125 + 4 + 3 = 12. Each part is worth 12,000/12=1,00012,000 / 12 = 1,000 manuscripts. Multiplying by each facility's ratio gives their total quota.
2
Calculate the number of manuscripts digitized by each facility in the first month.
Central: 3,0003,000; North: 1,8001,800; South: 2,1002,100.
Multiply each facility's allocated quota by their respective completion percentage (e.g., 60%60\% of 5,000=3,0005,000 = 3,000).
3
Calculate the number of manuscripts remaining to be digitized for each facility.
Central: 2,0002,000; North: 2,2002,200; South: 900900.
Subtract the number of digitized manuscripts from the initial quota for each facility.
4
Evaluate the accuracy of the given statements using the extracted data.
The total digitized is 3,000+1,800+2,100=6,9003,000 + 1,800 + 2,100 = 6,900. North remaining (2,2002,200) is greater than Central remaining (2,0002,000).
Comparing the processed numbers against the claims confirms which statements are factually correct based on the passage.

Key Concept

Extracting proportional allocations and applying distinct percentage rates to multi-entity caselet data.
Estimated Time:2m 0s
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Topics

Caselets and Paragraph-Based Data

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