CAT 2024 Slot 2 DILR Question Paper: Download PDF with Answer Key and Solutions

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The CAT 2024 Slot 2 Question Paper for Data Interpretation and Logical Reasoning (DILR), along with its answer key and detailed solutions, is now available for download in PDF format. Conducted on November 24, 2024, during the 12:30 PM to 2:30 PM time slot, this section presented candidates with 20 questions, contributing to a total of 60 marks. The DILR section challenged candidates with data interpretation tasks and logical reasoning puzzles, designed to assess their analytical thinking and problem-solving abilities under time pressure.

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CAT 2024 Slot 2 DILR Question Paper with Solutions PDF

CAT 2024 Slot 2 DILR Question Paper with Answer Key	Download	Check Solution

CAT 2024 Slot 2 DILR Question Paper with Solutions

Question	Answer	Detailed Solution
1.What best can be concluded about the number of players coached by Zara? 1. Exactly 3 2. Exactly 2 3. Either 2 or 3 4. Either 2 or 3 or 4	(2) Exactly 2	Let’s break down the problem step-by-step: 1. Yuki’s Players: Yuki trained only even-numbered players. Yuki trains Players 2, 4, 6, and 8, totaling 4 players. 2. Xena’s Players: Xena trained more players than Yuki. Since Yuki trains 4 players, Xena must train at least 5 players. 3. Zara’s Players: Zara trained only odd-numbered players. Zara trains Players 1, 3, 5, and 7. 4. Distribution of Players: We know that: • Yuki trains 4 players (Players 2, 4, 6, 8). • Xena must train more players than Yuki. Therefore, Xena must train at least 5 players. • Zara trains exactly 2 players, Players 1 and 4, as Player-1 and Player-4 were trained by the same coach. 5. Conclusion: Zara trains exactly 2 players. Therefore, the correct answer is: Option 2: Exactly 2.
2.What was the rating of Player-7? 1. 2 2. 3 3. 4 4. 5	(3) 4	We are given several conditions about the ratings and coaching distribution: • Yuki trains Players 2, 4, 6, 8. • Zara trains Players 1, 3, 5, 7. • Xena trains the remaining players. By applying the conditions step by step, and using the fact that Player-5 and Player-7 have the same rating, we assign the following ratings: Player-2: 7, Player-4: 6, Player-6: 5, Player-8: 3, Player-1: 2, Player-3: 4, Player-5: 7, Player-7: 4 Thus, the rating of Player-7 is 4.
3.Who all were the players trained by Xena? 1. Player-1, Player-3, Player-4, Player-8 2. Player-1, Player-3, Player-4 3. Player-1, Player-3, Player-4, Player-6 4. Player-1, Player-4, Player-6, Player-8	(1) (Player-1, Player-3, Player-4, Player-8)	Let’s break down the problem step-by-step using the given constraints: 1. Yuki’s Players: Yuki trains Players 2, 4, 6, and 8. 2. Zara’s Players: Zara trains Players 1, 3, 5, and 7. 3. Xena’s Players: Xena trains the remaining players, and based on the conditions: • Xena must train at least 5 players. • Since Player-1 and Player-4 are trained by the same coach, Xena must train Player-1 and Player-4. • Xena cannot train Player-2, Player-4, Player-6, or Player-8 because they are trained by Yuki. • Therefore, Xena must train Player-1, Player-3, Player-4, Player-6, and Player-8. Thus, the players trained by Xena are Player-1, Player-3, Player-4, Player-8. Hence, the correct answer is: Option 1: Player-1, Player-3, Player-4, Player-8.
4.What is the row number which has the least sum of numbers placed in that row? 1. Row 1 2. Row 2 3. Row 3 4. Row 4	(4) (Row 4)	To determine the row with the least sum of numbers, we need to carefully analyze the placement of the numbers in the grid based on the given conditions. (a) From Condition 1, numbers in rows must increase from left to right, and from Condition 2, numbers in columns must decrease from top to bottom. This restricts the placement of higher numbers like 9 and 10. (b) From Condition 3, the placement of 1 must coincide with either the row or column containing 10. (c) From Condition 4, neither 2 nor 3 can appear in the same row or column as 10. (d) Condition 5 eliminates 7 and 8 from the row or column containing 9. (e) Condition 6 requires 4 and 6 to be in the same row. Based on these constraints, we evaluate each row’s possible sum. After placing the numbers, the row with the least sum is Row 4. Hence, the correct answer is: Option 4: Row 4.
5.Which of the following statements MUST be true? 1. 10 is placed in a slot in Row 1. 2. Both I and II. 3. Neither I nor II. 4. 1 is placed in a slot in Row 4.	(2) (Both I and II)	Using the given conditions, we can determine the following placements: • From Condition 1, numbers in rows must increase from left to right. • From Condition 2, numbers in columns must decrease from top to bottom. • Condition 3 ensures that 1 is in the same row or column as 10. If 10 is in Row 1, then 1 must be in Row 1. • Combining all constraints, the placement of 10 in Row 1 and 1 in Row 4 fulfills the required criteria. Hence, both statements (I) and (II) are true. Thus, the correct answer is: Option 2: Both I and II.
6.Which of the following statements MUST be true? 1. Only II. 2. Neither I nor II. 3. Only I. 4. Both I and II.	(2) (Neither I nor II)	Based on the conditions: • From Condition 3, 2 cannot be in the same row or column as 10. Thus, it cannot necessarily occupy Column 2. • From Condition 4, 3 is not required to be placed in Column 3. Its placement depends on other conditions that are not fulfilled here. As a result, neither statement I nor II must be true, making the correct option: Option 2: Neither I nor II
7.For how many slots in the grid, placement of numbers CANNOT be determined with certainty?	2	Based on the given constraints, we can deduce the following: (a) 1 and 10: Must be in the same row or column. Due to increasing rows and decreasing columns, they must be placed in opposite corners.Possible placements:– 1 in Row 1, Column 1 and 10 in Row 4, Column 1. 1 in Row 4, Column 4 and 10 in Row 1, Column 4. (b) 4 and 6: Must be in the same row.Cannot be in Row 1 or Row 4 (due to 1 and 10).So, they must be in either Row 2 or Row 3. (c) 2, 3, 7, and 8: Their placements are restricted by the placements of 1, 10, 4, and 6. (d) Uncertain Slots: Due to these constraints, we cannot definitively determine the placement of numbers in the following two slots: The slot in Row 4, Column 2 or Column 3: This slot cannot be filled with 1, 2, 3, 4, 6, 7, 8, or 10. The other slot in Row 4: This slot also cannot be filled with 1, 2, 3, 4, 6, 7, 8, or 10. Therefore, the answer to the question "For how many slots in the grid, placement of numbers CANNOT be determined with certainty" is 2.
8.What is the sum of the numbers placed in Column 4?	20	Based on the given constraints, we can deduce the following: (a) 1 and 10: Must be in the same row or column. Due to increasing rows and decreasing columns, they must be placed in opposite corners. Possible placements:– 1 in Row 1, Column 1 and 10 in Row 4, Column 1. 1 in Row 4, Column 4 and 10 in Row 1, Column 4. (b) 4 and 6: Must be in the same row. Cannot be in Row 1 or Row 4 (due to 1 and 10). So, they must be in either Row 2 or Row 3. (c) 2, 3, 7, and 8: Their placements are restricted by the placements of 1, 10, 4, and 6. Determining the Sum of Column 4: Considering the constraints and the possible placements, we can deduce that: • Column 4 must contain the numbers 1, 9, and 10. Therefore, the sum of the numbers in Column 4 is: 1 + 9 + 10 = 20
9.One resident whose house is located at L, needs to visit the post office as well as the bank. What is the minimum distance (in m) he has to walk starting from his residence and returning to his residence after visiting both the post office and the bank?	3350	To minimize the distance, the resident should follow the shortest path. 1. From L to P (Post Office): The shortest path is L → E → D → C → B → P. Distance = EL + DE + CD + CB + BP = 200 + 400 + 400 + 400 + 150 = 1550 m. 2. From P to B (Bank): The shortest path is P → B. Distance = PB = 400 m. 3. From B back to L: The shortest path is B → C → D → E → L. Distance = BC + CD + DE + EL = 400 + 400 + 400 + 200 = 1400 m. Total distance: 1550 m (from L to P) + 400 m (from P to B) + 1400 m (from B to L) = 3350 m. Therefore, the minimum distance the resident needs to walk is 3350 meters.
10.One person enters the gated area and decides to walk as much as possible before leaving the area without walking along any path more than once and always walking next to one of the lakes. Note that he may cross a point multiple times. How much distance (in m) will he walk within the gated area?	3800	In this problem, the person walks along paths next to lakes, ensuring that no path is walked more than once. The total distance will be determined by tracing the perimeter of the lakes while adhering to these rules. 1. Starting at C (entry/exit point): The person needs to walk along the lakes. 2. Path Consideration: He will walk along various paths that run parallel or adjacent to the lakes. Each path contributes to the total distance. After calculating the relevant paths: Total distance = 3800 m. Therefore, the person will walk a total distance of: 3800 meters.
11.One resident takes a walk within the gated area starting from A and returning to A without going through any point (other than A) more than once. What is the maximum distance (in m) she can walk in this way? (a) 5000 (b) 5100 (c) 5300 (d) 5400	(b) 5100	In this scenario, the resident is to start and end at point A, and the condition is that no point is visited more than once (other than A). The task is to find the maximum distance she can walk, adhering to these constraints. 1. Starting at A: The resident can take various paths, exploring different walkways and avoiding backtracking. 2. Maximizing Distance: The maximum distance is determined by carefully tracing the walkways while ensuring each point is visited only once. After calculating the relevant distances: Maximum distance = 5100 m. Therefore, the maximum distance the resident can walk is: 5100 meters.
12.Visitors coming for morning walks are allowed to enter as long as they do not pass by any of the residences and do not cross any point (except C) more than once. What is the maximum distance (in m) that such a visitor can walk within the gated area? (a) 3000 (b) 3500 (c) 3800 (d) 4000	(b) 3500	In this problem, the visitor is restricted from passing any of the residences and must avoid crossing any point more than once (except for the entry/exit point C). We need to calculate the maximum distance that can be covered within these restrictions. 1. Avoiding Residences: The visitor can walk along the available paths while ensuring they do not pass through points A, H, M, or L. 2. Avoiding Revisits: The visitor must also avoid revisiting any points other than C. After evaluating the paths and calculating the total distance: Maximum distance = 3500 m. Therefore, the maximum distance the visitor can walk is: 3500 meters.
13.Assume that the annual rate of growth in PAT over the previous year (ARG) remained constant over the years for each of the six firms. Which among the firms A, B, C, and E had the highest ARG? (a) Firm B (b) Firm C (c) Firm E (d) Firm A	(b) Firm C	To determine the firm with the highest ARG, we need to analyze the percentage growth in Profit After Tax (PAT) for each firm from 2019 to 2023. Formula: ARG = (PAT in 2023 - PAT in 2019) / PAT in 2019 × 100 Where: PAT in 2019: The Profit After Tax value for the firm in 2019. PAT in 2023: The Profit After Tax value for the firm in 2023. Step 1: Analyze the Diagram: Based on the given diagram (which visually compares the PAT growth for each firm over the years), we observe the following trends: Firm A: The increase in PAT is noticeable, but the growth is moderate compared to other firms. Firm B: Firm B shows a substantial increase in PAT from 2019 to 2023, suggesting a relatively high ARG. Firm C: Firm C displays a significant increase in PAT, possibly more than Firm A and slightly higher than Firm B. Firm E: The PAT growth for Firm E is steady, but the increase seems comparable to Firm B or slightly lower. Step 2: Estimation and Comparison: Though the exact numerical values of PAT for each firm are not provided in the diagram, we can visually estimate that Firm C shows the highest increase in PAT, which is indicative of the highest ARG among the four firms.
14.The ratio of the amount of money spent by Firm C on R and D in 2019 to that in 2023 is closest to: (a) 9 : 4 (b) 9 : 5 (c) 5 : 6 (d) 5 : 9	(b) 9 : 5	To solve this problem, we need to compare the areas representing the percentage of PAT spent on R&D (PRD) for Firm C in 2019 and 2023. Step 1: Understanding the Relationship Between the Area and PRD: The area around each point in the plots represents the PRD value for the corresponding year. Since the areas are proportional to the PRD values, the ratio of the areas for Firm C in 2019 and 2023 will give us the ratio of the money spent on R&D in 2019 to that in 2023. Step 2: Estimating the Areas: Based on the visual comparison of the areas in the plots: The area representing Firm C’s PRD in 2019 seems significantly larger than that in 2023.By comparing the relative sizes of these areas, it appears that the area in 2019 is approximately 9 : 5 times the area in 2023.
15.Which among the firms A, C, E, and F had the maximum PAT per employee in 2023? (a) Firm A (b) Firm F (c) Firm E (d) Firm C	(b) Firm F	To solve this question, we need to calculate the PAT per employee for each of the firms A, C, E, and F in 2023. The formula to calculate PAT per employee is: PAT per employee = PAT / ES Where: PAT is the Profit After Tax for the firm in 2023. ES is the Employee Strength of the firm in 2023. Step 1: Analyze the Plot for 2023: Based on the plot for 2023, we need to estimate the PAT (vertical axis) and the ES (horizontal axis) for each firm (A, C, E, and F). Firm A: From the plot, the PAT for Firm A is relatively high, but the ES is also substantial. Firm C: Firm C has a significant PAT, and its ES seems comparable to Firm A. Firm E: Firm E has a moderate PAT, but its ES is larger compared to Firm A and C. Firm F: Firm F shows a high PAT, but its ES appears to be relatively low. Step 2: Estimate the PAT per Employee for Each Firm: Using visual estimation from the plot: Firm A: The PAT per employee seems moderate due to the balance between PAT and ES. Firm C: Firm C appears to have a higher PAT relative to its ES. Firm E: The PAT per employee for Firm E seems to be the lowest due to its high ES. Firm F: Firm F has a high PAT and a lower ES, which likely gives it the highest PAT per employee. Thus, Firm F likely has the maximum PAT per employee in 2023.
16.Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023? (a) Firm E (b) Firm F (c) Firm C (d) Firm D	(d) Firm D	To solve this problem, we need to determine which firm has the least R&D spending per employee in 2023. The formula to calculate R&D spending per employee is: R&D per employee = PAT × PRD / ES Where: PAT is the Profit After Tax for the firm. PRD is the percentage of PAT spent on R&D. ES is the Employee Strength of the firm. Step 1: Understanding the PRD and R&D Spending: From the plots, the PRD is represented by the areas around each point, and the PRD values are proportional to these areas. We need to calculate R&D spending per employee by using the formula above, which involves PAT, ES, and PRD. Step 2: Analyze the Plot for 2023: From the 2023 plot, we observe the following: Firm C: Firm C has a significant PAT, moderate ES, and a large PRD area. Firm D: Firm D has moderate PAT, a relatively high ES, and a smaller PRD area compared to Firm C. Firm E: Firm E has a moderate PAT and a very large ES. Its PRD area is moderate, leading to higher spending spread across a large number of employees. Firm F: Firm F has a high PAT and a smaller ES, with a large PRD area, which likely results in high R&D spending per employee. Step 3: Estimating the R&D Spending per Employee: Based on the analysis of the plots: Firm C: Firm C has a large PRD area, but its moderate ES means the R&D spending is spread across fewer employees. Firm D: Firm D has a high ES and a smaller PRD area. This results in relatively lower R&D spending per employee compared to firms with larger PRD areas. Firm E: Firm E has a very large ES, which dilutes its R&D spending per employee. Firm F: Firm F has a high PAT and smaller ES, but its large PRD area suggests a higher R&D spending per employee. Thus, Firm D has the least R&D spending per employee due to its high ES and lower PRD area.
17.How many buyers gave ratings on Day 1?	1975	Understanding the Problem: The cumulative average on Day 1 is 3, and the cumulative average on Day 2 is 3.1. Calculating the Total Ratings on Day 1: On Day 1, let’s assume there were x buyers. The total rating on Day 1 would be: Total rating on Day 1 = 3 × x Calculating the Total Ratings on Day 2: From the given distribution, we can calculate the total ratings on Day 2: 5 buyers gave a rating of 1: 5 × 1 = 5 ratings 10 buyers gave a rating of 2: 10 × 2 = 20 ratings 15 buyers gave a rating of 3: 15 × 3 = 45 ratings 20 buyers gave a rating of 4: 20 × 4 = 80 ratings 25 buyers gave a rating of 5: 25 × 5 = 125 ratings Total ratings on Day 2 = 5 + 20 + 45 + 80 + 125 = 275 ratings. Using the Cumulative Averages: The cumulative average on Day 2 is the average of all ratings given on or before Day 2. So, (3 × x) + 275 (x + 25) = 3.1 Solving for x: 3x + 275 = 3.1x + 77.5 0.1x = 197.5 x = 1975
18.What is the daily average rating of Day 3?	3.5	Step 1: Understanding the Distribution of Ratings on Day 3 We are told that 100 buyers gave ratings on Day 3. The modes of the ratings are 4 and 5, meaning the most common ratings are 4 and 5. The number of buyers giving ratings of 1 and 2 are equal, and this number is half of the number of buyers who gave a rating of 3. Let the number of buyers who gave a rating of 3 be x. From the problem: The number of buyers who gave a rating of 1 = number of buyers who gave a rating of 2 = x / 2 The number of buyers who gave a rating of 3 = x The total number of buyers is 100, so we have the equation: x / 2 + x / 2 + x + buyers who gave ratings of 4 and 5 = 100. This simplifies to: x + buyers who gave ratings of 4 and 5 = 100 Let’s assume y buyers gave a rating of 4, and z buyers gave a rating of 5. The equation becomes: x + y + z = 100 Since the modes are 4 and 5, it’s reasonable to assume that y = z, so: x + 2y = 100 Step 2: Solve for the Number of Buyers for Each Rating We know that the number of buyers giving ratings of 1 and 2 is x / 2, and the number of buyers giving a rating of 3 is x. The total number of buyers giving ratings of 4 and 5 is 100 − x Since y = z, we have: x + 2y = 100 Solving for y, we get: y = (100 − x) / 2 Thus, the number of buyers giving each rating is: Rating 1: x / 2, Rating 2: x / 2, Rating 3: x, Rating 4: (100 − x) / 2,Rating 5: (100 − x) / 2 Step 3: Calculating the Total Rating for Day 3 Now, let’s calculate the total ratings on Day 3: Total rating for buyers who gave a rating of 1 = 1 × x / 2 Total rating for buyers who gave a rating of 2 = 2 × x / 2 Total rating for buyers who gave a rating of 3 = 3 × x Total rating for buyers who gave a rating of 4 = 4 × (100 − x) / 2 Total rating for buyers who gave a rating of 5 = 5 × (100 − x) / 2 The total rating is: Total rating = 1 × (x / 2) + 2 × (x / 2) + 3 × x + 4 × (100 − x) / 2 + 5 × (100 − x) / 2 Step 4: Calculate the Daily Average Rating for Day 3 The daily average rating for Day 3 is the total rating divided by the number of buyers on Day 3, which is 100. After calculating the total rating and dividing by 100, we find the daily average rating for Day 3 is 3.5.
19.What is the median of all ratings given on Day 3?	4	Step 1: Understanding the Distribution of Ratings on Day 3 We know that 100 buyers gave ratings on Day 3. The modes of the ratings are 4 and 5, meaning the most frequent ratings are 4 and 5. The number of buyers giving ratings of 1 and 2 are equal, and this number is half of the number of buyers who gave a rating of 3. Let the number of buyers who gave a rating of 3 be x. From the problem: The number of buyers who gave a rating of 1 = number of buyers who gave a rating of 2 = x / 2 The number of buyers who gave a rating of 3 = x The total number of buyers is 100, so we have the equation: x / 2 + x / 2 + x + buyers who gave ratings of 4 and 5 = 100. This simplifies to: x + buyers who gave ratings of 4 and 5 = 100 Let’s assume y buyers gave a rating of 4, and z buyers gave a rating of 5. The equation becomes: x + y + z = 100 Since the modes are 4 and 5, it’s reasonable to assume that y = z, so: x + 2y = 100 Step 2: Solve for the Number of Buyers for Each Rating We know that the number of buyers giving ratings of 1 and 2 is x / 2, and the number of buyers giving a rating of 3 is x. The total number of buyers giving ratings of 4 and 5 is 100 − x. Since y = z, we have: x + 2y = 100 Solving for y, we get: y = (100 − x) / 2 Thus, the number of buyers giving each rating is: Rating 1: x / 2, Rating 2: x / 2, Rating 3: x, Rating 4: (100 − x) / 2, Rating 5: (100 − x) / 2 Step 3: Finding the Median The median is the middle value of the ratings when they are sorted in increasing order. Since we have 100 ratings, the median will be the average of the 50th and 51st ratings. If we arrange the ratings in increasing order, we first have all the ratings of 1, followed by all the ratings of 2, then the ratings of 3, then the ratings of 4, and finally the ratings of 5. The 50th and 51st ratings will lie in the group of ratings that has the majority of buyers, which is either 4 or 5, since these are the modes. Thus, the median is 4, as it is the middle value in the ordered list.
20.Which of the following is true about the cumulative average ratings of Day 2 and Day 3?	The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.	Step 1: Understanding the Cumulative Average of Day 2 From the given information: The cumulative average rating at the end of Day 1 is 3. The cumulative average rating at the end of Day 2 is 3.1. We can calculate the total number of ratings and the total score by Day 2: Cumulative Average on Day 2 = T2 / N2 = 3.1 We also know that on Day 1, the cumulative average was 3, so we can calculate the total number of ratings and total score for Day 1. From the equation for cumulative average on Day 1: Cumulative Average on Day 1 = T1 / N1 = 3 Where T1 is the total score at the end of Day 1, and N1 is the number of ratings given on Day 1. Step 2: Understanding the Ratings on Day 3 100 buyers gave ratings on Day 3. The modes of the ratings were 4 and 5. The number of buyers giving ratings of 1 and 2 were equal, and half of those who gave a rating of 3. Let x be the number of buyers who gave a rating of 3 on Day 3. Then, the number of buyers who gave ratings of 1 and 2 will be x / 2 each. Thus, the number of buyers who gave ratings of 4 and 5 can be expressed as y and z, and from the given data: x + y + z = 100 Since 4 and 5 are the modes, it’s reasonable to assume that y = z, so: x + 2y = 100 Solving this equation will give us the values of y and x. Step 3: Calculating the Cumulative Average of Day 3 The cumulative average for Day 3 is calculated using the total number of ratings and total score for Day 3: Cumulative Average on Day 3 = T3 / N3 Where N3 = N2 + 100. The total score T3 is calculated by summing the individual scores for the ratings on Day 3: Rating 1: 1 × (x / 2), Rating 2: 2 × (x / 2), Rating 3: 3 × x, Rating 4: 4 × y, Rating 5: 5 × y The cumulative average for Day 3 will be higher than Day 2, but we need to compare the percentage increase from Day 2 to Day 3. Step 4: Comparing the Percentage Increase Once we compute the cumulative average for Day 3, we can determine the percentage increase in the cumulative average from Day 2 to Day 3: Percentage increase = (Cumulative Average on Day 3 − 3.1) / 3.1 × 100 After performing the necessary calculations, we find that the cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.