Data Interpretation Practice Questions — State PSC Exam — Page 2

Question 21Question →

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 22Question →

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 23Question →

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 24Question →

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 25Question →

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 26Question →

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 27Question →

A technology company manufactured a total of $400$ units (where $1$ unit = $1,000$ smartphones) across five different models (M1, M2, M3, M4, and M5) in 2026.

The percentage distribution of the total smartphones manufactured is as follows:
M1: $25\%$
M2: $20\%$
M3: $30\%$
M4: $15\%$
M5: $10\%$

The following table shows the ratio of Domestic Sales to Exports for each model:

Model	Domestic Sales : Exports
M1	3 : 2
M2	1 : 3
M3	7 : 3
M4	1 : 2
M5	4 : 1

Based on the provided data, what is the positive difference between the number of M2 smartphones exported and the number of M4 smartphones sold domestically?

40,000

10,000

20,000

40

Show answer & explanation

Answer: $40,000$

Answer

40,000

The correct answer is found by first determining the true total (

400,000

), applying the percentages to find the production of M2 (

80,000

) and M4 (

60,000

), using the ratios to find M2 exports (

80,000 \times \frac{3}{4} = 60,000

) and M4 domestic sales (

60,000 \times \frac{1}{3} = 20,000

), and finally subtracting the two (

60,000 - 20,000 = 40,000

).

Step-by-Step Solution

1

Calculate the total number of smartphones manufactured.

400 \times 1,000 = 400,000

smartphones.

The unit multiplier must be applied to find the absolute base value before calculating model-specific quantities.

2

Calculate the total number of M2 and M4 smartphones manufactured.

M2 =

20\%

of

400,000 = 80,000

. M4 =

15\%

of

400,000 = 60,000

.

Applies the pie chart percentages to the total production.

3

Calculate the number of M2 smartphones exported.

Ratio is

1:3

, so export fraction is

\frac{3}{1+3} = \frac{3}{4}

. M2 Exported =

80,000 \times \frac{3}{4} = 60,000

.

Extracts the correct part of the ratio corresponding to exports.

4

Calculate the number of M4 smartphones sold domestically.

Ratio is

1:2

, so domestic fraction is

\frac{1}{1+2} = \frac{1}{3}

. M4 Domestic =

60,000 \times \frac{1}{3} = 20,000

.

Extracts the correct part of the ratio corresponding to domestic sales.

5

Find the positive difference between the two calculated values.

60,000 - 20,000 = 40,000

.

Answers the final question asked in the stem.

Key Concept

Combining percentage distribution data with ratio data to find absolute comparative values.

Question 28Question →

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 29Question →

A survey was conducted among $500$ civil service aspirants in a coaching institute regarding their daily newspaper reading habits among three publications: *The Hindu*, *The Indian Express*, and *Business Standard*.

The survey revealed the following data:
- The total number of aspirants reading *The Hindu*, *The Indian Express*, and *Business Standard* are $240$ , $210$ , and $180$ respectively.
- Exactly $20$ aspirants read all three newspapers.
- The ratio of the number of aspirants who read ONLY *The Hindu* and *The Indian Express* to those who read ONLY *The Indian Express* and *Business Standard* to those who read ONLY *The Hindu* and *Business Standard* is $3 : 2 : 4$ .
- The number of aspirants who read ONLY *Business Standard* is $70$ .
- The number of aspirants who read ONLY *The Hindu* is equal to the number of aspirants who read ONLY *The Indian Express*.

Based on the data provided, how many aspirants in total do NOT read any of the three newspapers?

45

65

35

55

Show answer & explanation

Answer: $45$

Answer

The total number of aspirants who do not read any of the three newspapers is 45.

By resolving the 7 disjoint regions of the Venn diagram using the given ratio

3k : 2k : 4k

, we find

k = 15

from the total for Business Standard (

180 = 70 + 4k + 2k + 20

). This yields exclusive intersection values of

45

,

30

, and

60

. Substituting these into the total for Indian Express (

210

) yields

\text{Only}(E) = 115

, which also equals

\text{Only}(H)

. Summing all seven disjoint regions gives

115 + 115 + 70 + 45 + 30 + 60 + 20 = 455

. Subtracting from the total population of

500

gives

45

aspirants who do not read any of the three newspapers.

Step-by-Step Solution

1

Define disjoint regions of the Venn diagram using given variables.

Let

H

,

E

, and

B

denote the sets of readers. Let

\text{Only}(H \cap E) = 3k

,

\text{Only}(E \cap B) = 2k

, and

\text{Only}(H \cap B) = 4k

. The center intersection

\text{All Three} = 20

.

Setting up explicit variables for mutually exclusive regions allows algebraic representation of total set sizes.

2

Calculate the ratio constant

k

using the total for set

B

(Business Standard).

|B| = \text{Only}(B) + \text{Only}(H \cap B) + \text{Only}(E \cap B) + \text{All Three} \implies 180 = 70 + 4k + 2k + 20 \implies 90 = 6k \implies k = 15

.

All sub-regions comprising set

B

are known except

k

, making it possible to solve for

k

directly.

3

Determine the exact counts of two-set exclusive intersections.

\text{Only}(H \cap E) = 3(15) = 45

,

\text{Only}(E \cap B) = 2(15) = 30

, and

\text{Only}(H \cap B) = 4(15) = 60

.

Multiplying the ratio multipliers by

k = 15

gives exact counts for each overlap.

4

Calculate

\text{Only}(E)

and

\text{Only}(H)

.

|E| = \text{Only}(E) + 45 + 30 + 20 = 210 \implies \text{Only}(E) = 115

. Since

\text{Only}(H) = \text{Only}(E)

,

\text{Only}(H) = 115

.

Subtracting known intersection counts of set

E

from

|E| = 210

gives

\text{Only}(E)

, which equals

\text{Only}(H)

.

5

Calculate the total number of aspirants who read at least one newspaper and find the complement.

|H \cup E \cup B| = 115 + 115 + 70 + 45 + 30 + 60 + 20 = 455

. Aspirants reading none

= 500 - 455 = 45

.

Summing all 7 disjoint regions gives the union. Subtracting the union from the universal set gives the number of aspirants reading no newspaper.

Key Concept

3-Set Principle of Inclusion-Exclusion and Disjoint Region Analysis

Question 30Question →

In a regional administrative office of $80$ officers, $45$ officers completed a training course in Data Analytics, $40$ officers completed a course in Public Policy, and $15$ officers completed both training courses. How many officers completed neither of the two training courses?

10

25

15

20

Show answer & explanation

Answer: $10$

Answer

10 officers completed neither of the two training courses.

To find the number of officers who completed neither course, calculate the union of the two sets using inclusion-exclusion:

n(\text{Data Analytics} \cup \text{Public Policy}) = 45 + 40 - 15 = 70

. The number of officers who completed neither course is the complement of this union relative to the total group:

80 - 70 = 10

.

Step-by-Step Solution

1

Identify the given set values and total universe

Total officers

n(U) = 80

, Data Analytics

n(A) = 45

, Public Policy

n(B) = 40

, Both

n(A \cap B) = 15

.

Establish baseline data to apply the set inclusion-exclusion principle.

2

Calculate the number of officers who completed at least one training course using the principle of inclusion-exclusion

n(A \cup B) = n(A) + n(B) - n(A \cap B) = 45 + 40 - 15 = 70

.

Avoid double-counting the officers who completed both courses.

3

Calculate the number of officers who completed neither course

n(\text{Neither}) = n(U) - n(A \cup B) = 80 - 70 = 10

.

Subtract the union of the two sets from the total population to find the complement set.

Key Concept

Two-set Principle of Inclusion-Exclusion and Complementary Sets

Estimated Time:45s

Question 31Question →

Is the positive integer $n$ divisible by $36$ ?

Statement I: $n^2$ is divisible by $108$ .
Statement II: $n^3$ is divisible by $576$ .

Which of the following options correctly describes the sufficiency of the statements?

Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.

Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient.

Either Statement I alone or Statement II alone is sufficient to answer the question.

Neither Statement I nor Statement II is sufficient to answer the question, and additional data is needed.

Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Show answer & explanation

Answer: Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Answer

Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Evaluating both statements together shows that Statement I requires

n

to be a multiple of

18

(

2^1 \times 3^2

) and Statement II requires

n

to be a multiple of

12

(

2^2 \times 3^1

). The least common multiple of

18

and

12

is

36

, which proves that

n

is guaranteed to be divisible by

36

. Neither statement alone provides both prime factor requirements.

Step-by-Step Solution

1

Analyze Statement I individually

Statement I states that

n^2

is divisible by

108 = 2^2 \times 3^3

. In the prime factorization of a square

n^2

, all exponents must be even numbers. Thus,

n^2

must contain at least

2^2

and

3^4

. Taking square roots,

n

must be a multiple of

2^1 \times 3^2 = 18

. If

n = 18

,

n

is NOT divisible by

36

. If

n = 36

,

n

IS divisible by

36

. Because we get both 'No' and 'Yes' answers, Statement I alone is NOT sufficient.

We must test if Statement I uniquely determines whether

n

is divisible by

36

.

2

Analyze Statement II individually

Statement II states that

n^3

is divisible by

576 = 2^6 \times 3^2

. In the prime factorization of a cube

n^3

, all exponents must be multiples of

3

. Thus,

n^3

must contain at least

2^6

and

3^3

. Taking cube roots,

n

must be a multiple of

2^2 \times 3^1 = 12

. If

n = 12

,

n

is NOT divisible by

36

. If

n = 36

,

n

IS divisible by

36

. Because we get both 'No' and 'Yes' answers, Statement II alone is NOT sufficient.

We must test if Statement II uniquely determines whether

n

is divisible by

36

.

3

Combine Statement I and Statement II

From Statement I,

n

contains at least

3^2

in its prime factorization. From Statement II,

n

contains at least

2^2

in its prime factorization. Combining these requirements,

n

must contain at least

2^2 \times 3^2 = 36

. Therefore,

n

is guaranteed to be divisible by

36

. Both statements together yield a definitive 'Yes'.

Evaluating both statements together combines the minimal necessary powers of each prime factor.

Key Concept

Data Sufficiency evaluation of prime factor exponents and divisibility rules

Estimated Time:2m 0s

Question 32Question →

The table below shows the annual wheat production (in metric tonnes) across four agricultural zones from 2021 to 2023:

Agricultural Zone	2021	2022	2023
Zone A	150	180	210
Zone B	200	250	300
Zone C	100	120	150
Zone D	300	330	360

Which of the following statements regarding the data given in the table are correct?

Select all that apply

Zone A registered a

20\%

growth in wheat production from 2021 to 2022.

In 2023, the wheat production of Zone B was exactly double that of Zone C.

The percentage increase in wheat production for Zone D from 2021 to 2022 was

15\%

.

Zone C produced a total of

400

metric tonnes of wheat over the three-year period from 2021 to 2023.

Show answer & explanation

Answer: Zone A registered a $20\%$ growth in wheat production from 2021 to 2022.; In 2023, the wheat production of Zone B was exactly double that of Zone C.

Answer

The correct statements are that Zone A registered a

20\%

growth in wheat production from 2021 to 2022, and in 2023, the wheat production of Zone B was exactly double that of Zone C.

Zone A's production grew from

150

to

180

tonnes, which is a growth of

\frac{30}{150} \times 100\% = 20\%

. In 2023, Zone B produced

300

tonnes while Zone C produced

150

tonnes, making Zone B's production exactly double that of Zone C.

Step-by-Step Solution

1

Calculate the percentage growth for Zone A from 2021 to 2022.

Percentage increase =

\frac{180 - 150}{150} \times 100\% = 20\%

. Statement is correct.

To verify the growth statement for Zone A using the base year 2021 value (

150

).

2

Compare Zone B and Zone C production figures for the year 2023.

Zone B produced

300

tonnes and Zone C produced

150

tonnes. Ratio =

\frac{300}{150} = 2

. Statement is correct.

To check if Zone B production was double that of Zone C in 2023.

3

Calculate the percentage increase for Zone D from 2021 to 2022.

Percentage increase =

\frac{330 - 300}{300} \times 100\% = 10\% \neq 15\%

. Statement is incorrect.

To evaluate the claim regarding Zone D's percentage growth.

4

Calculate the total wheat production of Zone C across 2021, 2022, and 2023.

Total =

100 + 120 + 150 = 370

tonnes

\neq 400

tonnes. Statement is incorrect.

To verify the three-year total production claim for Zone C.

Key Concept

Tabular Data Interpretation and Percentage Growth Analysis

Question 33Question →

The table below details the renewable energy generation (in Gigawatt-hours, GWh) across four zones in 2025:

Zone	Solar	Wind	Hydro	Biomass
North	120	150	200	50
South	180	220	160	40
East	90	60	250	80
West	210	190	100	70

What is the total solar energy generation (in GWh) across all four zones combined in 2025?

Show answer & explanation

Answer: 600

Answer

The total solar energy generation across all four zones in 2025 is 600 GWh.

Summing the values in the Solar column (

120 + 180 + 90 + 210

) yields a total of

600

GWh.

Step-by-Step Solution

1

Locate and extract the values under the 'Solar' column for all four zones.

North = 120, South = 180, East = 90, West = 210.

The question asks specifically for total solar energy generation.

2

Sum the extracted values across all rows.

120 + 180 + 90 + 210 = 600

GWh.

Combining values across all four zones yields the overall total for the solar category.

Key Concept

Data Extraction and Summation from Tables

Question 34Question →

The following missing data table presents the annual cargo volume (in Thousand Metric Tonnes, TMT) handled across three terminals (Terminal A, Terminal B, and Terminal C) at a major seaport for three distinct cargo categories: Bulk Cargo, Liquid Cargo, and Containerized Cargo.

Terminal	Bulk Cargo	Liquid Cargo	Containerized Cargo	Total
Terminal A	120	—	150	450
Terminal B	—	210	180	500
Terminal C	160	140	—	420
Total	390	530	450	1370

Based on the table above, what is the volume of Liquid Cargo (in Thousand Metric Tonnes) handled by Terminal A?

Show answer & explanation

Answer: 180

Answer

The volume of Liquid Cargo handled by Terminal A is 180 Thousand Metric Tonnes.

The row total for Terminal A is

450\text{ TMT}

. The known components are Bulk Cargo (

120\text{ TMT}

) and Containerized Cargo (

150\text{ TMT}

). Subtracting these from the total yields

450 - (120 + 150) = 180\text{ TMT}

. Alternatively, using the column total for Liquid Cargo (

530\text{ TMT}

) minus the Liquid Cargo of Terminal B (

210\text{ TMT}

) and Terminal C (

140\text{ TMT}

) gives

530 - 350 = 180\text{ TMT}

.

Step-by-Step Solution

1

Examine the row for Terminal A to find total cargo and known cargo types

Total cargo for Terminal A =

450\text{ TMT}

, Bulk Cargo =

120\text{ TMT}

, Containerized Cargo =

150\text{ TMT}

.

The sum of all cargo categories for a terminal equals the row total.

2

Calculate the sum of known cargo categories for Terminal A

120 + 150 = 270\text{ TMT}

.

Combining known entries simplifies finding the unknown value.

3

Subtract the sum of known categories from the row total

450 - 270 = 180\text{ TMT}

.

Liquid Cargo for Terminal A is the remaining portion of its total cargo volume.

4

Cross-verify using the column total for Liquid Cargo

Total Liquid Cargo =

530\text{ TMT}

. Liquid Cargo for Terminal B =

210\text{ TMT}

and Terminal C =

140\text{ TMT}

. Terminal A Liquid Cargo =

530 - (210 + 140) = 530 - 350 = 180\text{ TMT}

.

Cross-verification confirms numerical consistency.

Key Concept

Missing Data Interpretation via Row and Column Equations

Question 35Question →

The table below presents the operational metrics for Agricultural Processing Units across four districts of a state for FY 2025–26:

District	Total Processing Capacity (in '000 MT)	Operational Units Count	Total Raw Produce Received (in '000 MT)	Processing Efficiency Rate (%)
District A	450	18	360	$85\%$
District B	600	24	480	$90\%$
District C	500	20	420	$80\%$
District D	350	14	320	$75\%$

*Note: Processing Efficiency Rate is defined as the percentage of Total Raw Produce Received that is converted into finished products. The remaining portion of received raw produce is lost as processing waste.*

What is the overall average processing waste (in '000 Metric Tonnes) per operational unit across all four districts combined?

Show answer & explanation

Answer: 3.5

Answer

The overall average processing waste per operational unit across all four districts combined is

3.5

thousand Metric Tonnes.

The correct answer is derived by first finding the waste volume for each district based on raw produce received: District A (

360 \times 0.15 = 54

), District B (

480 \times 0.10 = 48

), District C (

420 \times 0.20 = 84

), and District D (

320 \times 0.25 = 80

). Summing these gives a combined total waste of

266

thousand MT. Dividing this total waste by the total count of operational units (

18 + 24 + 20 + 14 = 76

) yields

\frac{266}{76} = 3.5

thousand MT per unit.

Step-by-Step Solution

1

Calculate the processing waste percentage for each district

District A waste rate =

100\% - 85\% = 15\%

; District B waste rate =

100\% - 90\% = 10\%

; District C waste rate =

100\% - 80\% = 20\%

; District D waste rate =

100\% - 75\% = 25\%

.

Processing waste is the complement of processing efficiency rate.

2

Calculate total processing waste generated in each district in '000 MT

District A waste =

360 \times 0.15 = 54

'000 MT; District B waste =

480 \times 0.10 = 48

'000 MT; District C waste =

420 \times 0.20 = 84

'000 MT; District D waste =

320 \times 0.25 = 80

'000 MT.

Absolute waste is obtained by multiplying Total Raw Produce Received by the waste rate.

3

Calculate total waste and total operational units across all four districts combined

Total Waste =

54 + 48 + 84 + 80 = 266

'000 MT. Total Operational Units =

18 + 24 + 20 + 14 = 76

units.

Aggregating metrics across districts is required to find the combined weighted average.

4

Divide total combined waste by total combined operational units

Average Waste per Unit =

\frac{266}{76} = 3.5

'000 MT per unit.

Overall average metric equals total aggregate waste divided by total aggregate count of units.

Key Concept

Weighted Average and Percentage Calculation from Data Grids

Estimated Time:2m 30s

Question 36Question →

A train running at a constant speed crosses a stationary platform of length $200\text{ meters}$ . What is the speed of the train in $\text{km/h}$ ?

Statement I: The train takes $20\text{ seconds}$ to completely cross the platform.
Statement II: The train takes $8\text{ seconds}$ to cross a telegraph pole standing beside the track.

Which of the following options correctly describes the sufficiency of the statements to answer the question?

Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.

Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient.

Either Statement I alone or Statement II alone is sufficient to answer the question.

Neither Statement I alone nor Statement II alone is sufficient, and both statements together are not sufficient to answer the question.

Both Statement I and Statement II together are necessary and sufficient to answer the question.

Show answer & explanation

Answer: Both Statement I and Statement II together are necessary and sufficient to answer the question.

Answer

Both Statement I and Statement II together are necessary and sufficient to answer the question.

Evaluating each statement individually shows that neither Statement I nor Statement II alone provides enough information to determine the speed of the train because the length of the train remains unknown. However, combining both statements yields a system of two independent linear equations with two variables (length and speed of the train), allowing us to solve uniquely for the speed of the train (

60\text{ km/h}

). Therefore, both statements together are necessary and sufficient.

Step-by-Step Solution

1

Analyze Statement I alone.

Let the length of the train be

L\text{ meters}

and its speed be

v\text{ m/s}

. The equation is

L + 200 = 20v

. Since there are two unknowns (

L

and

v

), Statement I alone is not sufficient.

The length of the train is an unknown variable.

2

Analyze Statement II alone.

Crossing a telegraph pole means distance traveled equals the length of the train. The equation is

L = 8v

. Since there are two unknowns (

L

and

v

), Statement II alone is not sufficient.

The speed cannot be determined without knowing the length of the train.

3

Evaluate Statement I and Statement II together.

Substitute

L = 8v

into the first equation:

8v + 200 = 20v \implies 12v = 200 \implies v = \frac{50}{3}\text{ m/s}

. Converting to

\text{km/h}

:

v = \frac{50}{3} \times \frac{18}{5} = 60\text{ km/h}

. Thus, both statements together give a unique answer.

Two independent equations are sufficient to solve for two unknown variables.

Key Concept

Data Sufficiency evaluation for relative motion and distance-speed problems using linear equations.

Estimated Time:1m 30s

Question 37Question →

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 38Question →

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 39Question →

Two business partners, $A$ and $B$ , invested in a joint venture. What is the total profit earned by the business at the end of one year?

Statement I: Partner $A$ invested $\$6,000$ for the entire year, while Partner $B$ invested $\$9,000$ for $8$ months.
Statement II: Partner $A$ 's share of the annual profit is $\$2,400$ .

Which of the following options correctly describes the sufficiency of the statements to answer the question?

Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.

Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient.

Either Statement I alone or Statement II alone is sufficient to answer the question.

Neither Statement I nor Statement II is sufficient to answer the question.

Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Show answer & explanation

Answer: Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Answer

Both Statement I and Statement II together are sufficient to answer the question, but neither statement alone is sufficient.

Evaluating Statement I alone gives the profit-sharing ratio between Partner A and Partner B as

(6000 \times 12) : (9000 \times 8) = 1 : 1

, which is insufficient by itself to find the monetary profit. Statement II alone gives Partner A's profit share as

\$2,400

, which is also insufficient without knowing the proportion. Combining both statements shows that both partners receive equal shares, so total profit is

\$2,400 \times 2 = \$4,800

. Therefore, both statements together are necessary and sufficient.

Step-by-Step Solution

1

Evaluate Statement I alone

Profit sharing ratio of A to B =

(6000 \times 12) : (9000 \times 8) = 72,000 : 72,000 = 1 : 1

.

Profit is distributed in proportion to the product of capital invested and time period. Since no dollar amounts of profit are given, total profit cannot be determined from Statement I alone.

2

Evaluate Statement II alone

Partner A's profit share =

\$2,400

.

Without knowing Partner B's share or the ratio between their shares, the total profit cannot be calculated from Statement II alone.

3

Evaluate Statement I and Statement II together

Since ratio of shares is

1:1

and A's share is

\$2,400

, B's share is also

\$2,400

. Total profit =

\$2,400 + \$2,400 = \$4,800

.

Combining the ratio from Statement I and the monetary value from Statement II gives a unique answer to the question.

Key Concept

Partnership profit distribution ratio and data sufficiency evaluation

Question 40Question →

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.

Data Interpretation

Answer

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Key Concept

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