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CAT 2021 Slot 3 DILR · Set 3 of 4Data InterpretationEasy DifficultyQ13–Q16 · 4 MCQ

CAT 2021 Slot 3 DILR Set 3: Other Charts (4 Questions) with Solutions

The Other Charts set from the official CAT 2021 Slot 3 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 3 DILR · Questions 13–16
The figure above shows the schedule of four employees – Abani, Bahni, Danni and Tinni –whom Dhoni supervised in 2020. Altogether there were five projects which started and concluded in 2020 in which they were involved. For each of these projects and for each employee, the starting day was at the beginning of a month and the concluding day was the end of a month, and these are indicated by the left and right end points of the corresponding horizontal bars. The number within each bar indicates the percentage of assigned work completed by the employee for that project, as assessed by Dhoni.
For each employee, his/her total project-month (in 2020) is the sum of the number of months(s)he worked across the five project, while his/her annual completion index is the weight age average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months she worked in these projects. For each project, the total employee-month is the sum of the number of months four employees worked in this project, while its completion index is the weight age average of the completion percentage assigned for the employees who worked in this project, with the weights being the corresponding number of months they worked in this project.
Official Reference Chart - CAT 2021 Slot 3 Official Reference Chart - CAT 2021 Slot 3

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q13. Other Charts

MCQ · +3 / −1
Which of the following statements is/are true?
I: The total project-month was the same for the four employees.
II: The total employee-month was the same for the five projects.
  1. A) Only II
  2. B) Only I
  3. C) Neither I nor II
  4. D) Both I and II
Correct Answer
B) Only I
Step-by-step solution
📌 Core Concept
Read each bar's length in months from the chart, then add the months across employees (for statement I) and across projects (for statement II).
🔢 Step-by-Step Solution
1
Statement I needs each employee's months summed over all projects. A bar from the 1st of one month to the 1st of a later month spans the difference in months.
2
Abani: Project 1 runs Feb 1 to Apr 1 (2), Project 3 runs May 1 to Jul 1 (2), Project 4 runs Jul 1 to Dec 1 (5). Total 2+2+5=92+2+5=9.
3
Bahni: Project 1 (Feb 1 to Apr 1) is 2, Project 3 (Apr 1 to Aug 1) is 4, Project 5 (Oct 1 to Jan 1) is 3. Total 2+4+3=92+4+3=9.
4
Danni: Project 2 (Feb 1 to May 1) is 3, Project 3 (Jun 1 to Sep 1) is 3, Project 4 (Sep 1 to Nov 1) is 2, Project 5 (Dec 1 to Jan 1) is 1. Total 3+3+2+1=93+3+2+1=9.
5
Tinni: Project 1 (Jan 1 to Mar 1) is 2, Project 2 (Mar 1 to May 1) is 2, Project 4 (Jul 1 to Oct 1) is 3, Project 5 (Sep 1 to Nov 1) is 2. Total 2+2+3+2=92+2+3+2=9.
6
All four employees have 9 project-months, so statement I is true.
7
Statement II needs each project's employee-months. Project 1 has 2+2+2=62+2+2=6 (Abani, Bahni, Tinni). Project 2 has 3+2=53+2=5 (Danni, Tinni).
8
6≠56\neq 5, so the five projects do not have the same total employee-month. Statement II is false.
9
Only statement I is true.
Why Not the Others
A: Statement II fails because Project 1 has 6 employee-months and Project 2 has 5.
C: Statement I holds, since every employee has 9 months.
D: Statement II is false, so both cannot be true.
Quick Check
The four employee totals add to 4×9=364\times 9=36. The project totals should also add to 36. Project 3 has 2+4+3=92+4+3=9, Project 4 has 5+2+3=105+2+3=10, and Project 5 has 3+1+2=63+1+2=6. So 6+5+9+10+6=366+5+9+10+6=36, which confirms the readings. The project totals differ from each other.
Correct Answer: B

Q14. Other Charts

MCQ · +3 / −1
Which employees did not work in multiple projects for any of the months in 2020?
  1. A) Only Abani and Bahni
  2. B) Only Tinni
  3. C) All four of them
  4. D) Only Abani, Bahni and Danni
Correct Answer
D) Only Abani, Bahni and Danni
Step-by-step solution
Step-by-Step Solution:
1
Understanding the Problem:
Four employees (Abani, Bahni, Danni, Tinni) worked on five projects in 2020.
Each project's duration is represented by a horizontal bar, with the percentage completion indicated.
The goal is to determine which employees did not work on multiple projects in any given month.
2
Key Definitions:
Project-Month: The number of months an employee worked on projects.
Completion Index: Weighted average of completion percentages based on months worked.
3
Analyzing Overlaps:
Employees who did not work on multiple projects in any month have non-overlapping project durations.
If an employee's projects overlap in any month, they worked on multiple projects that month.
4
Determining the Answer:
The correct answer is D, indicating Abani, Bahni, and Danni did not work on multiple projects in any month.
Tinni must have worked on overlapping projects, hence working on multiple projects in some months.
Final Answer:
Correct Answer: D

Q15. Other Charts

MCQ · +3 / −1
The project duration, measured in terms of the number of months, is the time duringwhich at least one employee worked in the project. Which of the following pairs of theprojects had the same duration?
  1. A) Project 4, Project 5
  2. B) Project 3, Project 5
  3. C) Project 3, Project 4
  4. D) Project 1, Project 5
Correct Answer
C) Project 3, Project 4
Step-by-step solution
📌 Core Concept
A project's duration runs from the earliest start to the latest finish among its employees. Overlaps are counted once.
🔢 Step-by-Step Solution
1
Project 1: Tinni starts in Jan and Abani and Bahni finish at the end of Mar. The duration is Jan–Mar, which is 3 months.
2
Project 3:
Bahni starts on Apr 1.
Danni finishes at the end of Aug.
Abani's May–Jun bar lies inside this span.
The duration is Apr–Aug, which is 5 months.
3
Project 4:
Abani and Tinni both start on Jul 1.
Abani finishes at the end of Nov.
Danni's Sep–Oct bar lies inside this span.
The duration is Jul–Nov, which is 5 months.
4
Project 5:
Tinni starts on Sep 1.
Bahni finishes at the end of Dec.
The duration is Sep–Dec, which is 4 months.
5
Projects 3 and 4 both last 5 months. No other listed pair matches, because Project 5 lasts 4 and Project 1 lasts 3.
Why Not the Others
A) Project 4 is 5 months and Project 5 is 4.
B) Project 3 is 5 months and Project 5 is 4.
D) Project 1 is 3 months and Project 5 is 4.
Correct Answer: C

Q16. Other Charts

MCQ · +3 / −1
The list of employees in decreasing order of annual completion index is:
  1. A) Danni, Tinni, Bahni, Abani
  2. B) Danni, Tinni, Abani, Bahni
  3. C) Tinni, Danni, Abani, Bahni
  4. D) Bahni, Abani, Tinni, Danni
Correct Answer
B) Danni, Tinni, Abani, Bahni
Step-by-step solution
📌 Core Concept
An employee's annual completion index is the months-weighted average of the completion percentages. Every employee works 9 months in total, so the totals of (percentage × months) can be compared directly.
🔢 Step-by-Step Solution
1
Abani works 2 months at 100% (Project 1), 2 months at 100% (Project 3) and 5 months at 80% (Project 4). The sum is 200+200+400=800200+200+400=800, so the index is 800/9≈88.9800/9\approx 88.9.
2
Bahni works 2 months at 100% (Project 1), 4 months at 75% (Project 3) and 3 months at 90% (Project 5). The sum is 200+300+270=770200+300+270=770, so the index is 770/9≈85.6770/9\approx 85.6.
3
Danni works 3 months at 90% (Project 2), 3 months at 100% (Project 3), 2 months at 100% (Project 4) and 1 month at 100% (Project 5). The sum is 270+300+200+100=870270+300+200+100=870, so the index is 870/9≈96.7870/9\approx 96.7.
4
Tinni works 2 months at 80% (Project 1), 2 months at 100% (Project 2), 3 months at 100% (Project 4) and 2 months at 100% (Project 5). The sum is 160+200+300+200=860160+200+300+200=860, so the index is 860/9≈95.6860/9\approx 95.6.
5
In decreasing order, Danni (96.7), Tinni (95.6), Abani (88.9), Bahni (85.6).
Why Not the Others
A) and D) put Bahni above Abani, but Bahni's 75% in the 4-month Project 3 pulls the index down to 85.6.
C) puts Tinni above Danni, but Danni's 870 is higher than Tinni's 860.
Correct Answer: B
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CAT 2021 Slot 3 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

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