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Difficulty: HardCaselets and Paragraph-Based Data

In a state public health drive conducted across three administrative zones—Zone X, Zone Y, and Zone Z—a total of 12,00012,000 vaccines were administered. Zone X received 35%35\% of the total vaccines administered. In Zone Y, the total number of vaccines administered was 800800 more than that in Zone X, and the ratio of vaccines administered to children versus adults was 2:32 : 3. The remaining vaccines were administered in Zone Z, where 60%60\% of the recipients were adults and the rest were children. If 40%40\% of the recipients in Zone X were children, what is the total number of children who received vaccines across all three zones combined?

  1. A
    5,3605,360
  2. 4,8004,800Answer
  3. C
    7,9207,920
  4. D
    5,8005,800

Answer

4,8004,800 children received vaccines across all three zones combined.
The total vaccines administered across the three zones equal 12,00012,000. Zone X accounts for 35%35\% (4,2004,200 vaccines), of which 40%40\% are children (1,6801,680). Zone Y receives 800800 more than Zone X (5,0005,000 vaccines), with children making up 2/52/5 of this amount (2,0002,000). Zone Z receives the remaining 2,8002,800 vaccines, where 40%40\% are children (1,1201,120). Adding these together (1,680+2,000+1,1201,680 + 2,000 + 1,120) yields 4,8004,800.

Step-by-Step Solution

1
Calculate total vaccines and child recipients in Zone X
Total in Zone X = 0.35×12,000=4,2000.35 \times 12,000 = 4,200. Children in Zone X = 0.40×4,200=1,6800.40 \times 4,200 = 1,680.
Zone X receives 35%35\% of total vaccines, and 40%40\% of Zone X recipients are children.
2
Calculate total vaccines and child recipients in Zone Y
Total in Zone Y = 4,200+800=5,0004,200 + 800 = 5,000. Children in Zone Y = 22+3×5,000=25×5,000=2,000\frac{2}{2 + 3} \times 5,000 = \frac{2}{5} \times 5,000 = 2,000.
Zone Y receives 800800 more vaccines than Zone X, and children make up 22 parts out of 55 total parts.
3
Calculate total vaccines and child recipients in Zone Z
Total in Zone Z = 12,000−(4,200+5,000)=2,80012,000 - (4,200 + 5,000) = 2,800. Children percentage in Zone Z = 100%−60%=40%100\% - 60\% = 40\%. Children in Zone Z = 0.40×2,800=1,1200.40 \times 2,800 = 1,120.
Zone Z receives the remainder of total vaccines, and children constitute the remaining 40%40\% of Zone Z recipients.
4
Sum child recipients across all three zones
Total children = 1,680+2,000+1,120=4,8001,680 + 2,000 + 1,120 = 4,800.
Adding the child counts from Zone X, Zone Y, and Zone Z yields the final combined total.

Key Concept

Multi-step quantitative extraction, ratio division, and percentage base calculation from paragraph-based caselets.
Estimated Time:2m 30s
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Topics

Caselets and Paragraph-Based Data

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