Caselets and Paragraph-Based Data Practice Questions — State PSC Exam

Question 1Question →

A state tourism board recorded a total of $8,500$ visitors across three heritage sites—Site Alpha, Site Beta, and Site Gamma—during a cultural festival. The number of visitors to Site Alpha accounted for $40\%$ of the total visitors. Out of the visitors to Site Alpha, the ratio of domestic to international tourists was $3:2$ . Site Beta received $1,500$ fewer visitors than Site Alpha. At Site Beta, the number of international tourists was equal to the number of international tourists at Site Alpha. The remaining visitors went to Site Gamma, where $70\%$ were domestic tourists.

What is the difference between the total number of domestic tourists and the total number of international tourists across all three sites?

900

1,420

1,140

2,340

Show answer & explanation

Answer: $1,140$

Answer

The difference between the total number of domestic tourists and the total number of international tourists is

1,140

.

To find the final difference, the data must be extracted step-by-step for each site. Site Alpha has

3,400

visitors (

40\%

of

8,500

), splitting into

2,040

domestic and

1,360

international based on the

3:2

ratio. Site Beta has

1,900

visitors (

3,400 - 1,500

), with

1,360

international tourists (matching Alpha) and the remaining

540

being domestic. Site Gamma receives the leftover

3,200

visitors, of which

70\%

(

2,240

) are domestic and

960

are international. Summing the categories gives

4,820

domestic and

3,680

international tourists. The final difference is

4,820 - 3,680 = 1,140

.

Step-by-Step Solution

1

Calculate the tourist breakdown for Site Alpha.

Total =

3,400

. Domestic =

2,040

. International =

1,360

.

Site Alpha has

40\%

of

8,500

total visitors, which is

3,400

. The ratio of domestic to international is

3:2

. Domestic =

\frac{3}{5} \times 3,400 = 2,040

. International =

\frac{2}{5} \times 3,400 = 1,360

.

2

Calculate the tourist breakdown for Site Beta.

Total =

1,900

. International =

1,360

. Domestic =

540

.

Site Beta received

1,500

fewer visitors than Site Alpha, so

3,400 - 1,500 = 1,900

. The number of international tourists equals that of Site Alpha (

1,360

). The remaining

1,900 - 1,360 = 540

are domestic tourists.

3

Calculate the tourist breakdown for Site Gamma.

Total =

3,200

. Domestic =

2,240

. International =

960

.

Site Gamma received the remaining visitors:

8,500 - (3,400 + 1,900) = 3,200

. Since

70\%

are domestic, Domestic =

0.70 \times 3,200 = 2,240

. International =

3,200 - 2,240 = 960

.

4

Calculate overall totals and their difference.

Total Domestic =

4,820

. Total International =

3,680

. Difference =

1,140

.

Total Domestic =

2,040 + 540 + 2,240 = 4,820

. Total International =

1,360 + 1,360 + 960 = 3,680

. The difference is

4,820 - 3,680 = 1,140

.

Key Concept

Data Extraction and Sequential Problem Solving in Caselets

Question 2Question →

A State Public Service Commission conducted a detailed employment survey across three major districts: District A, District B, and District C. The total workforce across all three districts combined is $100,000$ .

- District A accounts for $40\%$ of the total workforce, and the ratio of male to female workers in District A is $3 : 2$ .
- District B has a total workforce that is $25\%$ greater than the total workforce of District A. Females constitute $44\%$ of District B's workforce.
- District C comprises the remaining workforce across the three districts, with a male-to-female ratio of $3 : 2$ .
- Across all three districts combined, $25\%$ of the total female workforce is employed in the government sector.
- Specifically, $30\%$ of females in District A and $20\%$ of females in District B are employed in the government sector, while the remaining government-employed females work in District C.

Based on the given information, what is the ratio of the number of female government sector workers in District C to the total number of male workers across all three districts combined?

13 : 580

13 : 236

13 : 60

1 : 40

Show answer & explanation

Answer: $13 : 580$

Answer

The ratio of the number of female government sector workers in District C to the total number of male workers across all three districts combined is

13 : 580

.

The total female government workers across all districts is 10,500 (25% of 42,000 total females). Subtracting District A's 4,800 and District B's 4,400 yields 1,300 government females in District C. The total male population across all three districts is 58,000 (24,000 + 28,000 + 6,000). The ratio 1,300 : 58,000 simplifies directly to 13 : 580.

Step-by-Step Solution

1

Calculate total workforce and gender breakdown for District A

Total workforce of District A =

40\%

of

100,000 = 40,000

. With a Male:Female ratio of

3:2

, Male workforce =

\frac{3}{5} \times 40,000 = 24,000

and Female workforce =

\frac{2}{5} \times 40,000 = 16,000

.

Establishing District A numbers is required as the baseline for District B and total female count.

2

Calculate total workforce and gender breakdown for District B

Workforce of District B =

1.25 \times 40,000 = 50,000

. Female workforce =

44\%

of

50,000 = 22,000

. Male workforce =

50,000 - 22,000 = 28,000

.

District B's population is given relative to District A.

3

Determine workforce and gender breakdown for District C

Workforce of District C =

100,000 - (40,000 + 50,000) = 10,000

. With Male:Female ratio of

3:2

, Male workforce =

\frac{3}{5} \times 10,000 = 6,000

and Female workforce =

\frac{2}{5} \times 10,000 = 4,000

.

District C contains the residual workforce from the total

100,000

.

4

Calculate overall male and female workforce totals

Total Male workforce =

24,000 + 28,000 + 6,000 = 58,000

. Total Female workforce =

16,000 + 22,000 + 4,000 = 42,000

.

The total male workforce forms the denominator of the required ratio.

5

Calculate government-employed females in District C

Total Female Government Workers =

25\%

of

42,000 = 10,500

. District A Female Government Workers =

30\%

of

16,000 = 4,800

. District B Female Government Workers =

20\%

of

22,000 = 4,400

. District C Female Government Workers =

10,500 - (4,800 + 4,400) = 1,300

.

Subtracting District A and B government females from the overall total isolates District C's count.

6

Compute the final ratio

Ratio =

\frac{1,300}{58,000} = \frac{13}{580}

or

13 : 580

.

Simplifying the fraction gives the required final ratio.

Key Concept

Multi-step quantitative interpretation of paragraph data involving percentage base shifts and system of equations.

Estimated Time:3m 0s

Question 3Question →

In a state public infrastructure development scheme for the fiscal year 2025–26, a total budget of ₹ $9,000$ crore was allocated across four major sectors: Agriculture Irrigation, Highway Expansion, Solar Infrastructure, and Rural Electrification.

Agriculture Irrigation received $28\%$ of the total allocated budget. The budget allocated to Highway Expansion was $37.5\%$ more than the budget allocated to Agriculture Irrigation. The remaining allocated budget was divided between Solar Infrastructure and Rural Electrification in the ratio $5 : 4$ .

Regarding the actual expenditures recorded at the end of the fiscal year:
- Agriculture Irrigation utilized $85\%$ of its allocated funds.
- Highway Expansion utilized $92\%$ of its allocated funds.
- Solar Infrastructure had an unspent budget of ₹ $315$ crore.
- Rural Electrification spent an amount equal to $1.25$ times the unspent budget of Agriculture Irrigation.

Based on the information provided, what is the total unspent budget across all four sectors combined, expressed in crore rupees?

Show answer & explanation

Answer: 1837.7

Answer

The total unspent budget across all four sectors combined is 1837.7 crore rupees.

By accurately deriving each sector's allocation from the given base percentage, percentage increment, and ratio, and then computing the respective unspent components according to the expenditure conditions, the total unspent amount is determined to be 1837.7 crore rupees.

Step-by-Step Solution

1

Calculate allocations for Agriculture Irrigation and Highway Expansion

Agriculture Irrigation = ₹2,520 crore; Highway Expansion = ₹3,465 crore

Agriculture Irrigation receives 28% of 9,000 crore = 2,520 crore. Highway Expansion gets 37.5% more than Agriculture Irrigation, which is 2,520 * (1 + 0.375) = 3,465 crore.

2

Calculate allocations for Solar Infrastructure and Rural Electrification

Solar Infrastructure = ₹1,675 crore; Rural Electrification = ₹1,340 crore

Remaining budget = 9,000 - (2,520 + 3,465) = 3,015 crore. Dividing 3,015 in ratio 5:4 gives (5/9)*3,015 = 1,675 crore for Solar and (4/9)*3,015 = 1,340 crore for Rural Electrification.

3

Determine unspent amounts for each sector individually

Agriculture Irrigation Unspent = ₹378 crore; Highway Expansion Unspent = ₹277.2 crore; Solar Infrastructure Unspent = ₹315 crore; Rural Electrification Unspent = ₹867.5 crore

15% of Agriculture Irrigation budget is unspent = 0.15 * 2,520 = 378 crore. 8% of Highway Expansion budget is unspent = 0.08 * 3,465 = 277.2 crore. Solar unspent is given as 315 crore. Rural Electrification expenditure is 1.25 * 378 = 472.5 crore, leaving 1,340 - 472.5 = 867.5 crore unspent.

4

Sum unspent amounts across all four sectors

Total Unspent Budget = ₹1,837.7 crore

Summing unspent amounts: 378 + 277.2 + 315 + 867.5 = 1,837.7 crore rupees.

Key Concept

Multi-step caselet data extraction, ratio division, percentage calculation, and aggregation

Question 4Question →

In an agricultural extension survey conducted across three blocks—Block A, Block B, and Block C—a total of $800$ farmers were interviewed regarding their adoption of organic farming practices. Out of the total interviewed farmers, $40\%$ were from Block A. The remaining farmers were equally divided between Block B and Block C. How many farmers were interviewed from Block B?

240

320

480

160

Show answer & explanation

Answer: $240$

Answer

The number of farmers interviewed from Block B is

240

.

The total number of interviewed farmers is

800

. Block A accounts for

40\%

of

800

, which equals

320

farmers. The remaining farmers across Block B and Block C combined total

800 - 320 = 480

. Since these remaining farmers are divided equally between Block B and Block C, Block B has

480 \div 2 = 240

farmers.

Step-by-Step Solution

1

Calculate the number of farmers in Block A

40\% \text{ of } 800 = 0.40 \times 800 = 320

farmers.

Block A accounts for

40\%

of the total

800

farmers.

2

Calculate the remaining number of farmers for Block B and Block C combined

800 - 320 = 480

farmers.

The paragraph states that the remaining farmers belong to Block B and Block C.

3

Divide the remaining farmers equally to find the count for Block B

480 \div 2 = 240

farmers.

Block B and Block C share the remaining farmers equally.

Key Concept

Paragraph Data Extraction and Simple Multi-Step Calculation

Estimated Time:45s

Question 5Question →

In a university central library, a survey was conducted on $500$ students who visited on Monday. Out of the total $500$ students, $300$ students borrowed books, while the remaining $200$ students used the reading room only. Among the students who borrowed books, $180$ were undergraduate students and the rest were postgraduate students. Among the students who used the reading room only, $120$ were undergraduate students and the rest were postgraduate students.

Based on the information provided in the paragraph above, which of the following statements are correct?

Select all that apply

The total number of postgraduate students surveyed is

200

.

The ratio of undergraduate students to postgraduate students who borrowed books is

3 : 2

.

The percentage of postgraduate students among those using the reading room only is

50\%

.

The total number of undergraduate students surveyed is

250

.

Show answer & explanation

Answer: The total number of postgraduate students surveyed is $200$ .; The ratio of undergraduate students to postgraduate students who borrowed books is $3 : 2$ .

Answer

The correct statements are that the total number of postgraduate students surveyed is 200, and the ratio of undergraduate students to postgraduate students who borrowed books is 3 : 2.

The total number of postgraduate students surveyed is

200

(

120

who borrowed books and

80

who used the reading room only). Furthermore, the ratio of undergraduate borrowers (

180

) to postgraduate borrowers (

120

) simplifies correctly to

3 : 2

.

Step-by-Step Solution

1

Extract data for students who borrowed books

Total borrowing books =

300

. Undergraduate borrowers =

180

. Postgraduate borrowers =

300 - 180 = 120

.

Separating the borrowing group into undergraduate and postgraduate categories.

2

Extract data for students using the reading room only

Total reading room only =

200

. Undergraduate reading room users =

120

. Postgraduate reading room users =

200 - 120 = 80

.

Separating the reading room group into undergraduate and postgraduate categories.

3

Calculate total postgraduate and undergraduate counts across both categories

Total postgraduate students =

120 + 80 = 200

. Total undergraduate students =

180 + 120 = 300

.

Summing values across both activity categories to verify totals.

4

Verify ratios and percentages

Ratio of UG borrowers to PG borrowers =

180 : 120 = 3 : 2

. Percentage of PG students in reading room =

\frac{80}{200} \times 100 = 40\%

.

Testing each option statement against computed values.

Key Concept

Data Extraction and Tabulation from Caselets

Question 6Question →

During a public health immunization drive in a rural district, a total of $1,500$ vaccines were administered across three primary health centers: PHC Alpha, PHC Beta, and PHC Gamma. PHC Alpha administered $550$ vaccines, while PHC Beta administered $600$ vaccines. The remaining vaccines were administered by PHC Gamma. What is the total number of vaccines administered by PHC Gamma?

350

1,150

550

450

Show answer & explanation

Answer: $350$

Answer

The total number of vaccines administered by PHC Gamma is

350

.

The total number of vaccines administered across all three health centers is

1,500

. Adding the vaccines administered by PHC Alpha (

550

) and PHC Beta (

600

) yields a total of

1,150

. Subtracting

1,150

from

1,500

gives

350

vaccines administered by PHC Gamma.

Step-by-Step Solution

1

Calculate the total vaccines administered by PHC Alpha and PHC Beta combined.

550 + 600 = 1,150

vaccines

To find the remaining amount for PHC Gamma, first aggregate the given counts of the other two health centers.

2

Subtract the combined count from the grand total of vaccines administered.

1,500 - 1,150 = 350

vaccines

Subtracting the known portions from the total gives the remaining vaccines administered by PHC Gamma.

Key Concept

Data extraction and simple subtraction from paragraph-based caselets

Question 7Question →

A regional energy transition board reviewed the adoption of residential solar panels across three counties: County Alpha, County Beta, and County Gamma. At the beginning of $2025$ , there were a total of $4,000$ households equipped with solar panels across these three counties. The number of such households in County Alpha was $1,500$ . At that time, County Beta had $50\%$ more solar-equipped households than County Gamma.

Over the course of $2025$ , the number of solar-equipped households in County Alpha increased by $20\%$ , while County Gamma saw a $40\%$ increase. By the end of $2025$ , the total number of solar-equipped households across all three counties reached $5,000$ .

Based on the information provided, which of the following statements are correct?

Select all that apply

The percentage increase in solar-equipped households in County Beta during

2025

was

20\%

.

At the end of

2025

, the number of solar-equipped households in County Beta was

2,100

.

The ratio of the number of solar-equipped households in County Gamma to County Alpha at the end of

2025

was

7:9

.

The overall percentage growth in solar-equipped households across all three counties during

2025

was

20\%

.

Show answer & explanation

Answer: The percentage increase in solar-equipped households in County Beta during $2025$ was $20\%$ .; The ratio of the number of solar-equipped households in County Gamma to County Alpha at the end of $2025$ was $7:9$ .

Answer

The statements confirming that County Beta saw a

20\%

increase and that the final ratio of County Gamma to County Alpha was

7:9

are both correct.

The valid statements accurately reflect that County Beta's solar adoption increased by exactly

300

households from a base of

1,500

(a

20\%

rise), and the final counts for County Gamma (

1,400

) and County Alpha (

1,800

) produce a ratio of

7:9

.

Step-by-Step Solution

1

Determine the initial number of solar-equipped households for all three counties at the start of

2025

.

Total =

4,000

. Alpha =

1,500

. Remaining for Beta and Gamma =

4,000 - 1,500 = 2,500

. Let Gamma = G. Beta is

50\%

more, so Beta =

1.5G

. Equation:

1.5G + G = 2,500 \Rightarrow 2.5G = 2,500 \Rightarrow G = 1,000

. Thus, Beta =

1,500

.

Establishing the baseline data for each category is necessary before applying growth percentages.

2

Calculate the growth and final number of households for County Alpha and County Gamma.

Alpha increase =

0.20 \times 1,500 = 300

, so Alpha final =

1,800

. Gamma increase =

0.40 \times 1,000 = 400

, so Gamma final =

1,400

.

These figures are explicitly given as percentage increases in the text and are required to find the unknown variables.

3

Deduce the final number and percentage increase for County Beta.

Total increase = Final Total - Initial Total =

5,000 - 4,000 = 1,000

. Beta increase = Total increase - (Alpha increase + Gamma increase) =

1,000 - (300 + 400) = 300

. Beta final =

1,500 + 300 = 1,800

. Beta percentage increase =

(300 / 1,500) \times 100\% = 20\%

.

Using the overall total allows extraction of the missing piece of data through subtraction.

4

Evaluate all provided statements against the extracted data.

County Beta's growth was

20\%

(True). County Beta's final count was

1,800

, not

2,100

(False). Gamma to Alpha final ratio is

1,400:1,800 = 7:9

(True). Overall total growth is

1,000 / 4,000 = 25\%

, not

20\%

(False).

Comparing the mathematical findings directly to the given options determines the correct answers.

Key Concept

Extracting quantitative variables from paragraph text and executing multi-step percentage calculations.

Question 8Question →

In a state e-governance initiative, a total of $2,400$ Common Service Centers (CSCs) are distributed across three districts: District P, District Q, and District R. District P contains $30\%$ of the total CSCs. The ratio of the total number of CSCs in District Q to those in District R is $4:3$ . Each CSC is operated by either a male or a female entrepreneur. In District P, $25\%$ of the CSCs are operated by female entrepreneurs. The number of female-operated CSCs in District Q is $50\%$ more than the number of female-operated CSCs in District P. If the total number of female-operated CSCs across all three districts combined is $600$ , what is the ratio of male-operated CSCs in District Q to the female-operated CSCs in District R?

29:11

23:9

23:5

5:23

Show answer & explanation

Answer: $23:5$

Answer

The correct ratio is

23:5

.

Based on the text, District Q has a total of 960 CSCs and District P has 180 female-operated CSCs. Since District Q has 50% more female-operated CSCs than P, it has 270 female-operated CSCs. This leaves 690 male-operated CSCs in Q. Since the total female-operated CSCs across all districts is 600, District R has 600 - (180 + 270) = 150 female-operated CSCs. The ratio of male-operated CSCs in Q to female-operated CSCs in R is 690:150, which simplifies to 23:5.

Step-by-Step Solution

1

Calculate the total number of CSCs in each district.

District P = 720. District Q = 960. District R = 720.

District P has 30% of 2,400 = 720. The remaining 1,680 CSCs are divided between Q and R in a 4:3 ratio. District Q = (4/7) * 1,680 = 960. District R = (3/7) * 1,680 = 720.

2

Calculate the number of female-operated CSCs in Districts P and Q.

Female in P = 180. Female in Q = 270.

Female CSCs in P = 25% of 720 = 180. Female CSCs in Q is 50% more than in P, meaning 180 + (0.50 * 180) = 180 + 90 = 270.

3

Calculate the number of female-operated CSCs in District R.

Female in R = 150.

Total female CSCs = 600. Female in R = Total - (Female P + Female Q) = 600 - (180 + 270) = 600 - 450 = 150.

4

Calculate the number of male-operated CSCs in District Q.

Male in Q = 690.

Total CSCs in Q (960) - Female in Q (270) = 690.

5

Find the requested ratio.

23:5

Ratio of Male in Q to Female in R = 690 : 150. Dividing both sides by 30 gives 23 : 5.

Key Concept

Data Extraction and Percentage Multi-step Calculations in Caselets

Question 9Question →

In a state public health drive conducted across three administrative zones—Zone X, Zone Y, and Zone Z—a total of $12,000$ vaccines were administered. Zone X received $35\%$ of the total vaccines administered. In Zone Y, the total number of vaccines administered was $800$ more than that in Zone X, and the ratio of vaccines administered to children versus adults was $2 : 3$ . The remaining vaccines were administered in Zone Z, where $60\%$ of the recipients were adults and the rest were children. If $40\%$ of the recipients in Zone X were children, what is the total number of children who received vaccines across all three zones combined?

5,360

4,800

7,920

5,800

Show answer & explanation

Answer: $4,800$

Answer

4,800

children received vaccines across all three zones combined.

The total vaccines administered across the three zones equal

12,000

. Zone X accounts for

35\%

(

4,200

vaccines), of which

40\%

are children (

1,680

). Zone Y receives

800

more than Zone X (

5,000

vaccines), with children making up

2/5

of this amount (

2,000

). Zone Z receives the remaining

2,800

vaccines, where

40\%

are children (

1,120

). Adding these together (

1,680 + 2,000 + 1,120

) yields

4,800

.

Step-by-Step Solution

1

Calculate total vaccines and child recipients in Zone X

Total in Zone X =

0.35 \times 12,000 = 4,200

. Children in Zone X =

0.40 \times 4,200 = 1,680

.

Zone X receives

35\%

of total vaccines, and

40\%

of Zone X recipients are children.

2

Calculate total vaccines and child recipients in Zone Y

Total in Zone Y =

4,200 + 800 = 5,000

. Children in Zone Y =

\frac{2}{2 + 3} \times 5,000 = \frac{2}{5} \times 5,000 = 2,000

.

Zone Y receives

800

more vaccines than Zone X, and children make up

2

parts out of

5

total parts.

3

Calculate total vaccines and child recipients in Zone Z

Total in Zone Z =

12,000 - (4,200 + 5,000) = 2,800

. Children percentage in Zone Z =

100\% - 60\% = 40\%

. Children in Zone Z =

0.40 \times 2,800 = 1,120

.

Zone Z receives the remainder of total vaccines, and children constitute the remaining

40\%

of Zone Z recipients.

4

Sum child recipients across all three zones

Total children =

1,680 + 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

Question 10Question →

In a state disaster relief operation, a total of $1,200$ food packets were distributed among three relief camps: Camp A, Camp B, and Camp C. Camp A received $400$ packets, while Camp B received $150$ more packets than Camp A. The remaining food packets were distributed to Camp C. How many food packets were distributed to Camp C?

Show answer & explanation

Answer: 250

Answer

The total number of food packets distributed to Camp C is 250.

Camp A receives 400 packets. Camp B receives 150 more than Camp A, which equals 400 + 150 = 550 packets. Combined, Camp A and Camp B receive 400 + 550 = 950 packets. Subtracting 950 from the total allocation of 1,200 packets leaves 250 packets for Camp C.

Step-by-Step Solution

1

Identify the number of packets given to Camp A and calculate the packets given to Camp B.

Camp A = 400 packets; Camp B = 400 + 150 = 550 packets.

The paragraph states Camp B received 150 more packets than Camp A.

2

Calculate the total number of packets distributed to Camp A and Camp B together.

Total for Camp A and Camp B = 400 + 550 = 950 packets.

Adding the individual allocations of Camp A and Camp B.

3

Subtract the combined allocation of Camp A and Camp B from the overall total packets.

Camp C = 1200 - 950 = 250 packets.

The remaining packets out of the total 1,200 were given to Camp C.

Key Concept

Data extraction and step-by-step arithmetic computation from narrative caselets

Question 11Question →

Under a state renewable energy initiative, a total capacity of $15,000\text{ kW}$ of solar panels was installed across three districts: District Alpha, District Beta, and District Gamma. District Alpha was allocated $40\%$ of the total capacity. The capacity installed in District Beta was $\frac{3}{4}$ of that in District Alpha, while the remaining capacity was installed in District Gamma. In District Alpha, $60\%$ of the installed capacity consists of rooftop solar panels, and the remainder consists of ground-mounted panels. In District Beta, the ratio of rooftop solar capacity to ground-mounted solar capacity is $2 : 3$ . In District Gamma, the ground-mounted solar capacity exceeds the rooftop solar capacity by $1,500\text{ kW}$ .

Based on the provided information, which of the following statements regarding the solar panel capacity distribution are correct?

Select all that apply

The total rooftop solar capacity installed across all three districts is

6,900\text{ kW}

.

The ground-mounted solar capacity in District Gamma is exactly twice its rooftop solar capacity.

District Beta accounts for

35\%

of the total solar panel capacity installed across all three districts.

The ratio of total ground-mounted solar capacity to total rooftop solar capacity across all three districts is

27 : 23

.

Show answer & explanation

Answer: The total rooftop solar capacity installed across all three districts is $6,900\text{ kW}$ .; The ground-mounted solar capacity in District Gamma is exactly twice its rooftop solar capacity.; The ratio of total ground-mounted solar capacity to total rooftop solar capacity across all three districts is $27 : 23$ .

Answer

The statements confirming that total rooftop solar capacity is

6,900\text{ kW}

, ground-mounted capacity in District Gamma is twice its rooftop capacity, and the ratio of total ground-mounted to rooftop capacity is

27 : 23

are all correct.

Evaluating the data step by step shows that District Alpha has

3,600\text{ kW}

rooftop and

2,400\text{ kW}

ground-mounted capacity; District Beta has

1,800\text{ kW}

rooftop and

2,700\text{ kW}

ground-mounted capacity; District Gamma has

1,500\text{ kW}

rooftop and

3,000\text{ kW}

ground-mounted capacity. This confirms that total rooftop capacity is

6,900\text{ kW}

, District Gamma's ground-mounted capacity is twice its rooftop capacity (

3,000\text{ kW} = 2 \times 1,500\text{ kW}

), and the overall ratio of ground-mounted to rooftop capacity is

8,100 : 6,900 = 27 : 23

.

Step-by-Step Solution

1

Calculate total capacity allocation for each district.

Alpha =

40\% \text{ of } 15,000 = 6,000\text{ kW}

. Beta =

\frac{3}{4} \times 6,000 = 4,500\text{ kW}

. Gamma =

15,000 - (6,000 + 4,500) = 4,500\text{ kW}

.

Determining individual district totals is necessary to break down capacity by panel type.

2

Determine rooftop and ground-mounted capacities for District Alpha and District Beta.

District Alpha: Rooftop =

60\% \text{ of } 6,000 = 3,600\text{ kW}

, Ground =

2,400\text{ kW}

. District Beta: Ratio

2:3 \implies

Rooftop =

\frac{2}{5} \times 4,500 = 1,800\text{ kW}

, Ground =

\frac{3}{5} \times 4,500 = 2,700\text{ kW}

.

Applying given percentages and ratios yields the exact breakdown for Alpha and Beta.

3

Determine rooftop and ground-mounted capacities for District Gamma.

Let Rooftop =

R

and Ground =

G

. We have

G + R = 4,500

and

G - R = 1,500

. Solving gives

2G = 6,000 \implies G = 3,000\text{ kW}

and

R = 1,500\text{ kW}

.

Setting up simultaneous equations resolves the unknown components for Gamma.

4

Verify overall totals and evaluate each statement.

Total Rooftop =

3,600 + 1,800 + 1,500 = 6,900\text{ kW}

. Total Ground =

2,400 + 2,700 + 3,000 = 8,100\text{ kW}

. Gamma Ground/Rooftop ratio =

3,000 / 1,500 = 2

. Beta percentage of total =

4,500 / 15,000 = 30\%

. Ground to Rooftop ratio =

8,100 / 6,900 = 27 / 23

.

Direct comparison evaluates which statements are factually supported by the paragraph data.

Key Concept

Data extraction and simultaneous calculation from unstructured paragraph-based quantitative scenarios.

Question 12Question →

In a state sericulture development drive, three agricultural districts—District R, District S, and District T—produced a cumulative total of $3,000\text{ kg}$ of raw silk, consisting exclusively of Mulberry silk and Eri silk. Across all three districts combined, Mulberry silk accounted for $60\%$ of the total raw silk production. In District R, total raw silk production was $1,000\text{ kg}$ , of which $65\%$ was Mulberry silk. District S produced a total of $1,200\text{ kg}$ of raw silk with a Mulberry silk to Eri silk production ratio of $7 : 5$ . The remaining raw silk was produced in District T. What is the absolute difference between the quantity of Mulberry silk and the quantity of Eri silk produced in District T?

100\text{ kg}

150\text{ kg}

200\text{ kg}

50\text{ kg}

Show answer & explanation

Answer: $100\text{ kg}$

Answer

The absolute difference between Mulberry silk and Eri silk produced in District T is

100\text{ kg}

.

Total raw silk produced is

3,000\text{ kg}

, making total Mulberry silk

1,800\text{ kg}

(

60\%

) and total Eri silk

1,200\text{ kg}

. District R produces

650\text{ kg}

Mulberry and

350\text{ kg}

Eri silk. District S produces

700\text{ kg}

Mulberry and

500\text{ kg}

Eri silk. Consequently, District T produces

450\text{ kg}

Mulberry silk (

1,800 - 1,350

) and

350\text{ kg}

Eri silk (

1,200 - 850

). The difference between Mulberry and Eri silk in District T is

450 - 350 = 100\text{ kg}

.

Step-by-Step Solution

1

Calculate overall production totals for Mulberry and Eri silk

Total Mulberry silk =

60\% \text{ of } 3,000\text{ kg} = 1,800\text{ kg}

. Total Eri silk =

3,000\text{ kg} - 1,800\text{ kg} = 1,200\text{ kg}

.

Establishing aggregate category totals provides the basis to determine missing District T values.

2

Determine breakdown for District R and District S

District R: Total =

1,000\text{ kg}

, Mulberry =

65\% \times 1,000 = 650\text{ kg}

, Eri =

350\text{ kg}

. District S: Total =

1,200\text{ kg}

, Mulberry =

\frac{7}{12} \times 1,200 = 700\text{ kg}

, Eri =

\frac{5}{12} \times 1,200 = 500\text{ kg}

.

Extract specific entity values from given percentage and ratio conditions.

3

Derive Mulberry and Eri silk quantities for District T

District T Mulberry =

1,800 - (650 + 700) = 450\text{ kg}

. District T Eri =

1,200 - (350 + 500) = 350\text{ kg}

.

Subtracting known district totals from overall state totals yields District T quantities.

4

Calculate the absolute difference for District T

Difference =

450\text{ kg} - 350\text{ kg} = 100\text{ kg}

.

Directly answers the final prompt query.

Key Concept

Data extraction, multi-entity category balance, and multi-step quantitative calculation from unstructured paragraph data.

Question 13Question →

Under a State Skill Development Mission, a total of $4,500$ candidates were enrolled across three vocational sectors: IT & Electronics, Healthcare & Allied Sciences, and Textile & Apparel. The IT & Electronics sector accounted for $40\%$ of the total enrolled candidates. The ratio of candidates enrolled in Healthcare & Allied Sciences to those in Textile & Apparel was $7 : 8$ . Upon completion of the training, $65\%$ of the enrolled candidates in IT & Electronics successfully obtained certification. The number of certified candidates in Healthcare & Allied Sciences was equal to $80\%$ of the certified candidates in IT & Electronics. If the total number of certified candidates across all three sectors combined was $2,898$ , what percentage of the enrolled candidates in the Textile & Apparel sector successfully obtained certification?

Show answer & explanation

Answer: 55

Answer

The certification percentage of enrolled candidates in the Textile & Apparel sector is

55\%

.

To find the certification percentage for the Textile & Apparel sector, first determine the enrollment figures: IT & Electronics has

1,800

candidates (

40\%

of

4,500

), leaving

2,700

candidates split in a

7 : 8

ratio between Healthcare (

1,260

) and Textile (

1,440

). Next, calculate certified candidates: IT & Electronics has

1,170

certified (

65\%

of

1,800

), and Healthcare has

936

certified (

80\%

of

1,170

). Subtracting these from the total

2,898

certified candidates leaves

792

certified candidates in Textile & Apparel. Finally,

\frac{792}{1,440} \times 100\% = 55\%

.

Step-by-Step Solution

1

Calculate the number of candidates enrolled in IT & Electronics

Enrolled in IT & Electronics =

0.40 \times 4,500 = 1,800

candidates.

IT & Electronics accounts for

40\%

of the overall

4,500

candidates.

2

Determine enrollment in Healthcare & Allied Sciences and Textile & Apparel

Remaining candidates =

4,500 - 1,800 = 2,700

. Enrolled in Healthcare =

\frac{7}{15} \times 2,700 = 1,260

. Enrolled in Textile =

\frac{8}{15} \times 2,700 = 1,440

.

The remaining

2,700

candidates are distributed between Healthcare and Textile in the ratio

7 : 8

(total

15

parts).

3

Calculate certified candidates in IT & Electronics

Certified in IT & Electronics =

0.65 \times 1,800 = 1,170

candidates.

65\%

of the enrolled IT & Electronics candidates achieved certification.

4

Calculate certified candidates in Healthcare & Allied Sciences

Certified in Healthcare =

0.80 \times 1,170 = 936

candidates.

Healthcare certified candidates equal

80\%

of certified candidates in IT & Electronics.

5

Determine certified candidates in Textile & Apparel

Certified in Textile =

2,898 - (1,170 + 936) = 2,898 - 2,106 = 792

candidates.

Total certified across all sectors is

2,898

.

6

Compute the certification rate for Textile & Apparel

Certification percentage =

\left(\frac{792}{1,440}\right) \times 100\% = 55\%

.

Divide certified Textile candidates by total enrolled Textile candidates and convert to percentage.

Key Concept

Data extraction, ratio partitioning, and sequential percentage calculation from unstructured text caselets.

Question 14Question →

In a municipal solid waste management drive across three processing centers—Plant North, Plant South, and Plant East—a total of $10,000\text{ tonnes}$ of waste was processed in a month.

- Plant North processed $30\%$ of the total waste. Of the waste processed at Plant North, $60\%$ was biodegradable and the rest was non-biodegradable.
- Plant South processed $1.5$ times the amount of non-biodegradable waste processed by Plant North. The ratio of biodegradable to non-biodegradable waste processed at Plant South was $4 : 3$ .
- Plant East processed the remaining waste, with a ratio of biodegradable to non-biodegradable waste of $5 : 2$ .

Based on the information provided above, which of the following statements are correct?

Select all that apply

The total quantity of biodegradable waste processed across all three plants combined is

6,200\text{ tonnes}

.

The ratio of non-biodegradable waste processed by Plant South to that processed by Plant East is

9 : 4

.

Plant East processed

30\%

of the total waste collected across all three plants.

Plant South processed more non-biodegradable waste than the biodegradable waste processed by Plant North.

Show answer & explanation

Answer: The total quantity of biodegradable waste processed across all three plants combined is $6,200\text{ tonnes}$ .; The ratio of non-biodegradable waste processed by Plant South to that processed by Plant East is $9 : 4$ .

Answer

The statements confirming that total biodegradable waste across all plants is 6,200 tonnes and that the ratio of non-biodegradable waste between Plant South and Plant East is 9 : 4 are correct.

The total biodegradable waste is indeed

1,800 + 2,400 + 2,000 = 6,200\text{ tonnes}

, making the first statement correct. Furthermore, comparing non-biodegradable waste of Plant South (

1,800\text{ tonnes}

) and Plant East (

800\text{ tonnes}

) gives the ratio

1,800 : 800 = 9 : 4

, making the second statement correct.

Step-by-Step Solution

1

Calculate waste quantities for Plant North.

Total =

3,000\text{ tonnes}

; Biodegradable =

1,800\text{ tonnes}

; Non-biodegradable =

1,200\text{ tonnes}

.

Plant North processed

30\%

of

10,000\text{ tonnes} = 3,000\text{ tonnes}

. Biodegradable is

60\%

of

3,000 = 1,800\text{ tonnes}

, leaving

1,200\text{ tonnes}

non-biodegradable.

2

Calculate waste quantities for Plant South.

Non-biodegradable =

1,800\text{ tonnes}

; Biodegradable =

2,400\text{ tonnes}

; Total =

4,200\text{ tonnes}

.

Non-biodegradable at South is

1.5 \times 1,200 = 1,800\text{ tonnes}

. Given Bio : Non-bio ratio of

4 : 3

,

3\text{ parts} = 1,800\text{ tonnes} \implies 1\text{ part} = 600\text{ tonnes}

. Thus, Biodegradable =

4 \times 600 = 2,400\text{ tonnes}

.

3

Calculate waste quantities for Plant East.

Total =

2,800\text{ tonnes}

; Biodegradable =

2,000\text{ tonnes}

; Non-biodegradable =

800\text{ tonnes}

.

Remaining total waste =

10,000 - (3,000 + 4,200) = 2,800\text{ tonnes}

. Given Bio : Non-bio ratio of

5 : 2

, total parts =

7

.

1\text{ part} = 400\text{ tonnes}

. Biodegradable =

5 \times 400 = 2,000\text{ tonnes}

and Non-biodegradable =

2 \times 400 = 800\text{ tonnes}

.

4

Verify each statement against calculated values.

Total Biodegradable =

1,800 + 2,400 + 2,000 = 6,200\text{ tonnes}

(True). South Non-bio : East Non-bio =

1,800 : 800 = 9 : 4

(True). Plant East share =

2,800 / 10,000 = 28\%

(False). South Non-bio (

1,800

) vs North Bio (

1,800

) are equal (False).

Comparing calculated numerical values directly evaluates statement validity.

Key Concept

Caselet Data Extraction and Multi-Step Proportionate Allocation

Question 15Question →

A state public transport corporation operates a total of $500$ buses across three urban divisions: Division X, Division Y, and Division Z. Division X accounts for $40\%$ of the total fleet, Division Y accounts for $30\%$ , and Division Z operates the remaining buses. In Division X, $25\%$ of the buses are electric. In Division Y, the ratio of electric buses to non-electric buses is $2 : 3$ . In Division Z, the number of electric buses is equal to $50\%$ of the number of electric buses in Division X. What is the ratio of the total number of non-electric buses to the total number of electric buses across all three divisions combined?

73 : 27

27 : 73

29 : 21

13 : 7

Show answer & explanation

Answer: 73 : 27

Answer

The ratio of the total number of non-electric buses to the total number of electric buses across all three divisions combined is 73 : 27.

Division X has 200 buses with 50 electric buses. Division Y has 150 buses with 60 electric buses (using the 2:3 ratio). Division Z has 150 buses with 25 electric buses (50% of 50). Total electric buses equal 135, leaving 365 non-electric buses. The simplified ratio of non-electric to electric buses is 365 : 135 = 73 : 27.

Step-by-Step Solution

1

Calculate the total fleet size for each division

Division X =

40\%

of

500 = 200

buses; Division Y =

30\%

of

500 = 150

buses; Division Z =

500 - (200 + 150) = 150

buses.

Establishing the total fleet per division is required to extract category values.

2

Calculate electric buses in each division

Division X electric =

25\%

of

200 = 50

buses. Division Y electric =

\frac{2}{2+3} \times 150 = 60

buses. Division Z electric =

50\%

of

50 = 25

buses.

Extracting the electric bus count per division using the specified percentages and ratios.

3

Calculate total electric and non-electric buses combined

Total Electric =

50 + 60 + 25 = 135

buses. Total Non-Electric =

500 - 135 = 365

buses.

Summing values across all divisions to find overall totals.

4

Compute the required ratio of non-electric to electric buses

Ratio =

365 : 135 = 73 : 27

.

Simplifying the ratio by dividing both terms by their greatest common divisor,

5

.

Key Concept

Caselet Data Extraction and Multi-step Ratio & Percentage Calculations

Estimated Time:1m 30s

Question 16Question →

In a state handloom and textile development initiative, data was collected from three handicraft clusters: Cluster A, Cluster B, and Cluster C. A total of $1,200$ weavers are registered across these three clusters. The number of weavers in Cluster C is $300$ , of which $40\%$ are female. The number of weavers in Cluster A is $25\%$ more than the number of weavers in Cluster B. In Cluster B, the ratio of male to female weavers is $3:2$ . If the total number of female weavers across all three clusters is $480$ , what is the total number of male weavers registered in Cluster A?

Show answer & explanation

Answer: 300

Answer

The total number of male weavers registered in Cluster A is 300.

By determining the total weavers in Cluster A (500) and Cluster B (400), and finding the female counts in Cluster C (120) and Cluster B (160), we deduce that Cluster A has 200 female weavers. Subtracting 200 from the 500 total weavers in Cluster A leaves 300 male weavers.

Step-by-Step Solution

1

Determine total weavers in Clusters A and B combined

900 weavers

Subtract Cluster C weavers (300) from the overall total of 1,200 weavers.

2

Calculate weavers in Cluster B and Cluster A

Cluster B = 400 weavers, Cluster A = 500 weavers

Set Cluster A = 1.25 × Cluster B. Then 2.25 × Cluster B = 900, yielding Cluster B = 400 and Cluster A = 500.

3

Determine female weavers in Cluster C and Cluster B

Cluster C females = 120, Cluster B females = 160

40% of 300 is 120 for Cluster C. Based on the 3:2 male to female ratio in Cluster B, females account for 2/5 of 400, which is 160.

4

Calculate female weavers in Cluster A

200 female weavers

Subtract known females in B (160) and C (120) from the total 480 female weavers: 480 - (120 + 160) = 200.

5

Calculate male weavers in Cluster A

300 male weavers

Subtract female weavers in Cluster A from total weavers in Cluster A: 500 - 200 = 300.

Key Concept

Data extraction, multi-step ratio calculation, and percentage breakdown from paragraph caselets.

Question 17Question →

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

Select all that apply

The North Branch currently has a greater number of manuscripts left to digitize compared to the Central Library.

The three facilities combined successfully digitized a total of

6,900

manuscripts during the first month.

The South Branch accounted for exactly

70\%

of the total manuscripts digitized across all three facilities combined.

The Central Library digitized

1,200

fewer manuscripts than the North Branch during the first month.

Show answer & explanation

Answer: The North Branch currently has a greater number of manuscripts left to digitize compared to the Central Library.; The three facilities combined successfully digitized a total of $6,900$ manuscripts 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 = 6,900

manuscripts. Additionally, the North Branch has

2,200

manuscripts remaining (

4,000 - 1,800

), which is strictly greater than the Central Library's

2,000

remaining manuscripts (

5,000 - 3,000

).

Step-by-Step Solution

1

Calculate the initial allocation of manuscripts for each facility based on the

5:4:3

ratio.

Central Library:

5,000

; North Branch:

4,000

; South Branch:

3,000

.

The total ratio parts are

5 + 4 + 3 = 12

. Each part is worth

12,000 / 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:

3,000

; North:

1,800

; South:

2,100

.

Multiply each facility's allocated quota by their respective completion percentage (e.g.,

60\%

of

5,000 = 3,000

).

3

Calculate the number of manuscripts remaining to be digitized for each facility.

Central:

2,000

; North:

2,200

; South:

900

.

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 = 6,900

. North remaining (

2,200

) is greater than Central remaining (

2,000

).

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

Question 18Question →

A recent agricultural survey evaluated the annual yield of three crops—Wheat, Rice, and Maize—across two neighboring regions, Region Alpha and Region Beta. The combined yield of all three crops in both regions was $8,000$ metric tons. Region Alpha accounted for $55\%$ of the total combined yield. In Region Alpha, the yield of Maize was $800$ metric tons, and the remaining yield was distributed between Wheat and Rice in the ratio of $5:4$ , respectively. In Region Beta, the yield of Rice was exactly half of the Wheat yield in Region Alpha. Additionally, the Maize yield in Region Beta was $20\%$ higher than the Maize yield in Region Alpha.

Based on the survey data, what is the ratio of the Wheat yield in Region Beta to the total Maize yield from both regions combined?

41:24

44:41

41:44

47:38

Show answer & explanation

Answer: $41:44$

Answer

The ratio of the Wheat yield in Region Beta to the total Maize yield from both regions is

41:44

.

The correct ratio is determined by first finding the Wheat yield in Region Beta (

1,640

metric tons) and the total Maize yield from both regions combined (

1,760

metric tons). Simplifying the ratio

1,640 : 1,760

by dividing both values by

40

yields the final result of

41:44

.

Step-by-Step Solution

1

Determine the total crop yield for each region.

Region Alpha total =

4,400

tons; Region Beta total =

3,600

tons.

Region Alpha is

55\%

of the

8,000

total (

0.55 \times 8000 = 4400

). Region Beta is the remainder (

8000 - 4400 = 3600

).

2

Calculate the individual crop yields for Region Alpha.

Maize =

800

tons, Wheat =

2,000

tons, Rice =

1,600

tons.

Maize is given as

800

. The remainder for Wheat and Rice is

4,400 - 800 = 3,600

. Using the

5:4

ratio, Wheat is

\frac{5}{9} \times 3600 = 2000

, and Rice is

\frac{4}{9} \times 3600 = 1600

.

3

Calculate the individual crop yields for Region Beta.

Rice =

1,000

tons, Maize =

960

tons, Wheat =

1,640

tons.

Rice is half of Region Alpha's Wheat (

0.5 \times 2000 = 1000

). Maize is

20\%

higher than Region Alpha's Maize (

800 + 0.20 \times 800 = 960

). Wheat is the remainder of Region Beta's total (

3600 - 1000 - 960 = 1640

).

4

Calculate the required ratio.

The final ratio is

41:44

.

Total Maize from both regions is

800 + 960 = 1,760

. The ratio of Region Beta's Wheat to Total Maize is

1640 : 1760

, which simplifies to

164 : 176

, and further to

41 : 44

by dividing both numbers by

4

.

Key Concept

Extracting interrelated data points from a narrative caselet to compute multi-step ratios and percentages.

Question 19Question →

A multinational corporation allocated a total annual training budget of 140,000 dollars across its three major divisions: Sales, Information Technology (IT), and Human Resources (HR). According to the financial distribution guidelines, the IT division received exactly 20% more funding than the Sales division. Meanwhile, the HR division was allocated exactly half of the amount given to the IT division. If the HR division dedicates 40% of its allocated training budget specifically to onboarding programs, what is the exact amount (in dollars) spent by the HR division on onboarding?

Show answer & explanation

Answer: 12000

Answer

12000

By converting the text into an algebraic equation, we establish the Sales budget as

x

, IT as

1.2x

, and HR as

0.6x

. The sum

2.8x

equals 140,000 dollars, making

x = 50,000

. The HR division receives

0.6x

, which is 30,000 dollars. Finally, taking 40% of the HR division's 30,000 dollar budget yields 12,000 dollars for onboarding programs.

Step-by-Step Solution

1

Define algebraic variables for each division's allocation.

Sales =

x

, IT =

1.2x

, HR =

0.6x

To translate the relative proportional statements from the paragraph into a solvable mathematical model.

2

Set up an equation representing the total corporate training budget.

x + 1.2x + 0.6x = 140,000

The sum of the three divisional budgets must equal the total allocated amount.

3

Solve the equation for

x

to find the Sales division's baseline budget.

2.8x = 140,000 \Rightarrow x = 50,000

To isolate the base variable from which the other departmental budgets are derived.

4

Calculate the total training budget allocated specifically to the HR division.

HR =

0.6 \times 50,000 = 30,000

The question asks about a subset of the HR budget, so the total HR budget must be known first.

5

Calculate 40% of the HR division's budget.

0.40 \times 30,000 = 12,000

The paragraph specifies that exactly 40% of the HR training budget goes to onboarding programs.

Key Concept

Extracting quantitative relationships from text to form algebraic equations and calculating sequential percentages.

Question 20Question →

A municipal health department organized a vaccination drive across three different wards: Ward X, Ward Y, and Ward Z. The total population across the three wards is $12,000$ , and this population is distributed among Ward X, Ward Y, and Ward Z in the ratio of $5:4:3$ , respectively.

In Ward X, $60\%$ of the population received Dose 1, and out of those who received Dose 1, $40\%$ also received Dose 2. The number of people who received Dose 1 in Ward Y is equal to the number of people who received Dose 1 in Ward X. In Ward Y, the number of people who received Dose 2 is half the number of people who received Dose 1 in the same ward. In Ward Z, the number of people who received Dose 1 is $40\%$ less than the number of people who received Dose 1 in Ward X. Furthermore, $50\%$ of the individuals who received Dose 1 in Ward Z went on to receive Dose 2.

Based on this information, what is the ratio of the total number of people who received Dose 2 in Ward X and Ward Z combined to the number of people in Ward Y who did NOT receive Dose 1?

7:5

27:10

21:10

29:10

Show answer & explanation

Answer: $21:10$

Answer

The correct ratio is

21:10

.

Based on the given ratios and percentages, Ward X has

1,200

people with Dose 2, and Ward Z has

900

people with Dose 2, combining for

2,100

. Ward Y has a total population of

4,000

, and

3,000

received Dose 1, leaving exactly

1,000

people who did not receive Dose 1. The ratio is

2,100 : 1,000

, which simplifies to

21:10

.

Step-by-Step Solution

1

Calculate the total population for each ward based on the

5:4:3

ratio.

Total ratio parts =

5 + 4 + 3 = 12

. Multiplier =

12,000 \div 12 = 1,000

. Ward X population =

5 \times 1,000 = 5,000

. Ward Y population =

4 \times 1,000 = 4,000

. Ward Z population =

3 \times 1,000 = 3,000

.

Establishing the base population for each ward is necessary to apply the subsequent percentages.

2

Calculate Dose 1 and Dose 2 recipients for Ward X.

Dose 1 in X =

60\%

of

5,000 = 3,000

. Dose 2 in X =

40\%

of

3,000 = 1,200

.

The problem states

40\%

of those who received Dose 1 went on to get Dose 2, meaning the base for Dose 2 is the Dose 1 count, not the total population.

3

Calculate the relevant statistics for Ward Y.

Dose 1 in Y = Dose 1 in X =

3,000

. People in Y who did NOT receive Dose 1 = Total Y population - Dose 1 in Y =

4,000 - 3,000 = 1,000

.

The question asks for the number of people in Ward Y who did not receive Dose 1 to be used as the denominator in the final ratio.

4

Calculate Dose 1 and Dose 2 recipients for Ward Z.

Dose 1 in Z is

40\%

less than Dose 1 in X (

3,000

), which is

3,000 - (0.40 \times 3,000) = 1,800

. Dose 2 in Z =

50\%

of

1,800 = 900

.

This establishes the final required values needed for the numerator of the ratio.

5

Formulate and simplify the required ratio.

Ratio = (Dose 2 in X + Dose 2 in Z) : (No Dose 1 in Y) = (

1,200 + 900

) :

1,000 = 2,100 : 1,000 = 21:10

.

Combines the extracted data to answer the specific question asked in the stem.

Key Concept

Extracting and chaining percentage-based data across multiple entities to form relationships.

Caselets and Paragraph-Based Data

Answer

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Step-by-Step Solution

Key Concept

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Step-by-Step Solution

Key Concept