CAT 2021 Slot 3 · DILR · Set 2: Project Schedules of Four Employees

The full set and all 4 questions (Q5–Q8) from CAT 2021 Slot 3, with answers and solutions.

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 projects, while his/her annual completion index is the weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he 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 weightage 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.

Question 5 · Reasoning Based DI

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
    Both I and II
  3. C
    Neither I nor II
  4. D
    Only I
Pick an option, then check.
Answer & solution

Answer: Option D

Solving the set

Step 1 – Read every bar from the chart (each bar starts at the beginning of a month and ends at the end of a month).

Employee

Project 1

Project 2

Project 3

Project 4

Project 5

Total months

Abani

Feb–Mar (2), 100%

—

May–Jun (2), 100%

Jul–Nov (5), 80%

—

9

Bahni

Feb–Mar (2), 100%

—

Apr–Jul (4), 75%

—

Oct–Dec (3), 90%

9

Danni

—

Feb–Apr (3), 90%

Jun–Aug (3), 100%

Sep–Oct (2), 100%

Dec (1), 100%

9

Tinni

Jan–Feb (2), 80%

Mar–Apr (2), 100%

—

Jul–Sep (3), 100%

Sep–Oct (2), 100%

9

Employee-months

6

5

9

10

6

36

Duration

Jan–Mar (3)

Feb–Apr (3)

Apr–Aug (5)

Jul–Nov (5)

Sep–Dec (4)

Step 2 – Overlaps: Tinni's Project 4 (Jul–Sep) and Project 5 (Sep–Oct) overlap in September. No one else works on two projects in the same month.

Step 3 – Annual completion index = month-weighted average of completion percentages.

Employee

Weighted sum

Months

Annual completion index

Abani

2×100 + 2×100 + 5×80 = 800

9

88.9

Bahni

2×100 + 4×75 + 3×90 = 770

9

85.6

Danni

3×90 + 3×100 + 2×100 + 1×100 = 870

9

96.7

Tinni

2×80 + 2×100 + 3×100 + 2×100 = 860

9

95.6

This question

Total project-months: Abani 9, Bahni 9, Danni 9, Tinni 9 – Statement I true. Employee-months: P1 6, P2 5, P3 9, P4 10, P5 6 – Statement II false.

Hence, the answer is option 4.

Question 6 · Reasoning Based DI

Which employees did not work in multiple projects for any of the months in 2020?
  1. A
    Only Abani, Bahni and Danni
  2. B
    Only Abani and Bahni
  3. C
    All four of them
  4. D
    Only Tinni
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Read every bar from the chart (each bar starts at the beginning of a month and ends at the end of a month).

Employee

Project 1

Project 2

Project 3

Project 4

Project 5

Total months

Abani

Feb–Mar (2), 100%

—

May–Jun (2), 100%

Jul–Nov (5), 80%

—

9

Bahni

Feb–Mar (2), 100%

—

Apr–Jul (4), 75%

—

Oct–Dec (3), 90%

9

Danni

—

Feb–Apr (3), 90%

Jun–Aug (3), 100%

Sep–Oct (2), 100%

Dec (1), 100%

9

Tinni

Jan–Feb (2), 80%

Mar–Apr (2), 100%

—

Jul–Sep (3), 100%

Sep–Oct (2), 100%

9

Employee-months

6

5

9

10

6

36

Duration

Jan–Mar (3)

Feb–Apr (3)

Apr–Aug (5)

Jul–Nov (5)

Sep–Dec (4)

Step 2 – Overlaps: Tinni's Project 4 (Jul–Sep) and Project 5 (Sep–Oct) overlap in September. No one else works on two projects in the same month.

Step 3 – Annual completion index = month-weighted average of completion percentages.

Employee

Weighted sum

Months

Annual completion index

Abani

2×100 + 2×100 + 5×80 = 800

9

88.9

Bahni

2×100 + 4×75 + 3×90 = 770

9

85.6

Danni

3×90 + 3×100 + 2×100 + 1×100 = 870

9

96.7

Tinni

2×80 + 2×100 + 3×100 + 2×100 = 860

9

95.6

This question

From Step 2, only Tinni had an overlap (September, Projects 4 and 5). So Abani, Bahni and Danni never worked on two projects in a month.

Hence, the answer is option 1.

Question 7 · Reasoning Based DI

The project duration, measured in terms of the number of months, is the time during which at least one employee worked in the project. Which of the following pairs of the projects had the same duration?
  1. A
    Project 1, Project 5
  2. B
    Project 4, Project 5
  3. C
    Project 3, Project 5
  4. D
    Project 3, Project 4
Pick an option, then check.
Answer & solution

Answer: Option D

Solving the set

Step 1 – Read every bar from the chart (each bar starts at the beginning of a month and ends at the end of a month).

Employee

Project 1

Project 2

Project 3

Project 4

Project 5

Total months

Abani

Feb–Mar (2), 100%

—

May–Jun (2), 100%

Jul–Nov (5), 80%

—

9

Bahni

Feb–Mar (2), 100%

—

Apr–Jul (4), 75%

—

Oct–Dec (3), 90%

9

Danni

—

Feb–Apr (3), 90%

Jun–Aug (3), 100%

Sep–Oct (2), 100%

Dec (1), 100%

9

Tinni

Jan–Feb (2), 80%

Mar–Apr (2), 100%

—

Jul–Sep (3), 100%

Sep–Oct (2), 100%

9

Employee-months

6

5

9

10

6

36

Duration

Jan–Mar (3)

Feb–Apr (3)

Apr–Aug (5)

Jul–Nov (5)

Sep–Dec (4)

Step 2 – Overlaps: Tinni's Project 4 (Jul–Sep) and Project 5 (Sep–Oct) overlap in September. No one else works on two projects in the same month.

Step 3 – Annual completion index = month-weighted average of completion percentages.

Employee

Weighted sum

Months

Annual completion index

Abani

2×100 + 2×100 + 5×80 = 800

9

88.9

Bahni

2×100 + 4×75 + 3×90 = 770

9

85.6

Danni

3×90 + 3×100 + 2×100 + 1×100 = 870

9

96.7

Tinni

2×80 + 2×100 + 3×100 + 2×100 = 860

9

95.6

This question

From the duration row: Project 3 (April–August) and Project 4 (July–November) both last 5 months.

Hence, the answer is option 4.

Question 8 · Reasoning Based DI

The list of employees in decreasing order of annual completion index is:
  1. A
    Danni, Tinni, Bahni, Abani
  2. B
    Bahni, Abani, Tinni, Danni
  3. C
    Danni, Tinni, Abani, Bahni
  4. D
    Tinni, Danni, Abani, Bahni
Pick an option, then check.
Answer & solution

Answer: Option C

Solving the set

Step 1 – Read every bar from the chart (each bar starts at the beginning of a month and ends at the end of a month).

Employee

Project 1

Project 2

Project 3

Project 4

Project 5

Total months

Abani

Feb–Mar (2), 100%

—

May–Jun (2), 100%

Jul–Nov (5), 80%

—

9

Bahni

Feb–Mar (2), 100%

—

Apr–Jul (4), 75%

—

Oct–Dec (3), 90%

9

Danni

—

Feb–Apr (3), 90%

Jun–Aug (3), 100%

Sep–Oct (2), 100%

Dec (1), 100%

9

Tinni

Jan–Feb (2), 80%

Mar–Apr (2), 100%

—

Jul–Sep (3), 100%

Sep–Oct (2), 100%

9

Employee-months

6

5

9

10

6

36

Duration

Jan–Mar (3)

Feb–Apr (3)

Apr–Aug (5)

Jul–Nov (5)

Sep–Dec (4)

Step 2 – Overlaps: Tinni's Project 4 (Jul–Sep) and Project 5 (Sep–Oct) overlap in September. No one else works on two projects in the same month.

Step 3 – Annual completion index = month-weighted average of completion percentages.

Employee

Weighted sum

Months

Annual completion index

Abani

2×100 + 2×100 + 5×80 = 800

9

88.9

Bahni

2×100 + 4×75 + 3×90 = 770

9

85.6

Danni

3×90 + 3×100 + 2×100 + 1×100 = 870

9

96.7

Tinni

2×80 + 2×100 + 3×100 + 2×100 = 860

9

95.6

This question

From Step 3: Danni 96.7 > Tinni 95.6 > Abani 88.9 > Bahni 85.6.

Hence, the answer is option 3.

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →