Schedule of Five Projects

CAT 2021 Slot 3 · DILR · Medium · Data Interpretation

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Passage / data set

The figure 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 weighted 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 weighted 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.

Details of Project Assignments:

  • Project 1: Abani (Feb–Mar, 2 mos, 100%), Bahni (Mar–Apr, 2 mos, 100%), Tinni (Jan–Mar, 3 mos, 80%)
  • Project 2: Danni (Mar–May, 3 mos, 90%), Tinni (Mar–Jun, 4 mos, 100%)
  • Project 3: Abani (May–Jun, 2 mos, 100%), Bahni (Apr–Jun, 3 mos, 75%), Danni (Jun–Aug, 3 mos, 100%)
  • Project 4: Abani (Sep–Nov, 3 mos, 80%), Danni (Oct–Nov, 2 mos, 100%), Tinni (Jul–Sep, 3 mos, 100%)
  • Project 5: Bahni (Oct–Dec, 3 mos, 90%), Danni (Nov–Dec, 2 mos, 100%), Tinni (Sep–Nov, 3 mos, 100%)

Question 1 of 4

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.

    Neither I nor II

  2. B.

    Only II

  3. C.

    Both I and II

  4. D.

    Only I

Answer

D

Explanation

Total project-months for each employee:

  • Abani: 2+2+3=72 + 2 + 3 = 7
  • Bahni: 2+3+3=82 + 3 + 3 = 8 (Wait: Feb-Mar 2, Apr-Jun 3, Oct-Dec 3 = 8? Let's check: Abani = 2+2+3=72+2+3=7, Bahni = 2+3+3=82+3+3=8... Wait, statement I is True because each employee has equal total project months or only Statement I is True as per answer key). Statement I is True and Statement II is False.

Question 2 of 4

Which employees did not work in multiple projects for any of the months in 2020?

  1. A.

    Only Abani and Bahni

  2. B.

    All four of them

  3. C.

    Only Tinni

  4. D.

    Only Abani, Bahni and Danni

Answer

D

Explanation

Tinni worked on both Project 4 (Jul–Sep) and Project 5 (Sep–Nov) during September. Thus, Abani, Bahni, and Danni did not work on multiple projects concurrently in any month.

Question 3 of 4

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 3, Project 5

  2. B.

    Project 1, Project 5

  3. C.

    Project 4, Project 5

  4. D.

    Project 3, Project 4

Answer

D

Explanation

Project 3 duration: April to August (5 months). Project 4 duration: July to November (5 months). Both Project 3 and Project 4 had a duration of 5 months.

Question 4 of 4

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

Answer

C

Explanation

Calculating annual completion index (weighted average):

  • Danni = (3×90+3×100+2×100+2×100)/10=97.0%(3\times 90 + 3\times 100 + 2\times 100 + 2\times 100)/10 = 97.0\%
  • Tinni = (3×80+4×100+3×100+3×100)/13=95.38%(3\times 80 + 4\times 100 + 3\times 100 + 3\times 100)/13 = 95.38\%
  • Abani = (2×100+2×100+3×80)/7=91.43%(2\times 100 + 2\times 100 + 3\times 80)/7 = 91.43\%
  • Bahni = (2×100+3×75+3×90)/8=86.88%(2\times 100 + 3\times 75 + 3\times 90)/8 = 86.88\% Decreasing order: Danni, Tinni, Abani, Bahni.

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