There are 21 employees working in a division

There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE). During the next five months, the division has to complete five projects every month. Out of the 25 projects, 5 projects are "challenging", while the remaining ones are "standard". Each of the challenging projects has to be completed in different months. Every month, five teams - T1, T2, T3, T4 and T5, work on one project each. T1, T2, T3, T4 and T5 are allotted the challenging project in the first, second, third, fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest.

In the first month, T1 has one more SE than T2, T2 has one more SE than T3, T3 has one more SE than T4, and T4 has one more SE than T5. Between two successive months, the composition of the teams changes as follows:

a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team.

b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T4 to T2.

Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team.

1. The number of times in which the composition of team T2 and the number of times in which composition of team T4 remained unchanged in two successive months are:

  1. (2, 1)
  2. (1, 0)
  3. (0, 0)
  4. (1, 1)

2. The number of SE in T1 and T5 for the projects in the third month are, respectively: 

  1. (0, 2)
  2. (0, 3)
  3. (1, 2)
  4. (1, 3)

3. Which of the following CANNOT be the total credit points earned by any employee from the projects?

  1. 140
  2. 150
  3. 170
  4. 200

4. One of the employees named Aneek scored 185 points. Which of the following CANNOT be true?

  1. Aneek worked only in teams T1, T2, T3, and T4
  2. Aneek worked only in teams T1, T2, T4, and T5
  3. Aneek worked only in teams T2, T3, T4, and T5
  4. Aneek worked only in teams T1, T3, T4, and T5

Answers

  1. B
  2. A
  3. B
  4. D

There are 10 SE and 11 RE. In the first month, since T1 has one more SE than T2, who in turn has one more SE than T3, and so on, the number of SEs in T1, T2, T3, T4 and T5 must be 4, 3, 2, 1 and 0.

Also, the team that is assigned the challenging project has one more employee than the rest. Hence, the team that is assigned the challenging project will have 5 employees, while the other teams will have 4 employees.

Since T1 is assigned the Challenging project in the first month, T1 will have 5 employees, and the other teams will have 4 employees each.

The following table provides the composition of the teams in the first month:

Team SE RE Total
T1 4 1 5
T2 3 1 4
T3 2 2 4
T4 1 3 4
T5 0 4 4

In the second month, T2 will be allotted the challenging project.

From a, two SEs will be transferred from T1 to T2. One RE is transferred from T2 to T1. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to T1. Similar transfers will happen between T2 and T4.

The following table provides the number of employees in each team in the second month:

Team SE RE Total
T1 1 3 4
T2 4 1 5
T3 2 2 4
T4 2 2 4
T5 1 3 4

In the third month, T3 will be allotted the challenging project.

From a, two SEs will be transferred from T2 to T3. One RE is transferred from T3 to T2. From b, one SE will be transferred from T1 to T5, one RE will be transferred from T5 to T1. Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2.

The following table provides the number of employees in each team in the third month:

Team SE RE Total
T1 0 4 4
T2 1 3 4
T3 4 1 5
T4 3 1 4
T5 2 2 4

In the fourth month, T4 will be allotted the challenging project.

From a, two SEs will be transferred from T3 to T4. One RE is transferred from T4 to T3. From b, one SE must be transferred from T1 to T5. However, since there are no SEs in T1, this will not happen. Also, one SE must be transferred from T2 to T4 and one RE must be transferred from T4 to T2. However, there are no REs in T4. Hence, this transfer will not happen.

The following table provides the number of employees in each team in the fourth month:

Team SE RE Total
T1 0 4 4
T2 1 3 4
T3 2 2 4
T4 5 0 5
T5 2 2 4

In the fifth month, T5 will be allotted the challenging project. From a, two SEs will be transferred from T4 to T5. One RE is transferred from T5 to T4. From b, one SE must be transferred from T1 to T5. However, since there are no SEs in T1, this will not happen.

Also, one SE will be transferred from T2 to T4 and one RE will be transferred from T4 to T2. The following table provides the number of employees in each team in the fifth month:

Team SE RE Total
T1 0 4 4
T2 0 4 4
T3 2 2 4
T4 4 0 4
T5 4 1 5

1. The composition of T2 did not change once between the third and the fourth months. The composition of T4 changed between any two successive months.

2. Number of SE in T1 in third month = 0; Number of SE in T5 in third month = 2.

3. Challenging projects has 200 credits and standard projects have 100 credits. In each type of project, the credits are equally shared by the employees in the team. Hence, for a challenging project an employee earns 200/5 = 40 credits. For a standard project, an employee earns 100/4 = 25 credits.

For the five months, an employee can work in five challenging projects OR four challenging projects and one standard project OR three challenging projects and two standard projects OR two challenging projects and three challenging projects OR one challenging project and four standard projects OR five standard projects.

In each case, an employee will earn 200 or 185 or 170 or 155 or 140 or 125 credits. Hence, it is not possible for an employee to earn 150 credits.

4. Since Aneek secured 185 credits, he worked in four challenging projects and one standard project.

Option A: Aneek could have worked in T1 in first month (in challenging project), T2 in second month (in challenging project), T3 in third month (in challenging project), T4 in fourth month (in challenging project) and fifth month (in standard project). Hence, this is possible.

Option B: Aneek could have worked in T1 in first month (in challenging project), T2 in second month (in challenging project), T4 in third month (in standard project), T4 in fourth month (in challenging project) and T5 in fifth month (in challenging project). Hence, this is possible.

Option C: Aneek could have worked in T2 in first month (in standard project), T2 in second month (in challenging project), T3 in third month (in challenging project), T4 in fourth month (in challenging project) and T5 in fifth month (in challenging project). Hence, this is possible.

Option D: Aneek could have worked in T1 in first month (in challenging project). He can work in T1 or T5 in the second month. In either case, he cannot work in T3 without working in T2 first. If we assume, he worked in T3 in the first month, he could not have worked in four teams in the five months. Similarly, we can rule out the other possibilities for this option. Hence, this is the answer.