Question

The number of times in which the composition of team T 2 and the number of times in which composition of team T 4 remained unchanged in two successive months are:

• A. (2, 1)
• B. (1, 0)
• C. (0, 0)
• D. (1, 1)
• A. (0, 2)
• B. (0, 3)
• C. (1, 2)
• D. (1, 3)
• A. 140
• B. 150
• C. 170
• D. 200
• A. Aneek worked only in teams T1, T2, T3, and T4
• B. Aneek worked only in teams T1, T2, T4, and T5
• C. Aneek worked only in teams T2, T3, T4, and T5
• D. Aneek worked only in teams T1, T3, T4, and T5

Answer 1

The Correct Option is B

Given that 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, … till T5, 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 presents 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 illustrates 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 illustrates 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.
 

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

From option b, the transfer of one SE from T1 to T5 is required. However, since there are no SEs in T1, this transfer cannot occur. Additionally, one SE must be transferred from T2 to T4, and one RE must be transferred from T4 to T2. Nevertheless, since there are no REs in T4, this transfer is not feasible. Therefore, these specific transfers do not take place.

The subsequent table outlines the employee count for each team in the fourth month. In the fifth month, the challenging project is assigned to T5. As per option a, two SEs are moved from T4 to T5, and one RE is relocated from T5 to T4. Despite the requirement for one SE to be transferred from T1 to T5 according to option b, this action cannot be executed due to the absence of SEs in T1. Additionally, one SE will be transferred from T2 to T4, and one RE will be transferred from T4 to T2.

The following table illustrates the number of employees in each team for 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

There was no alteration in the makeup of T2 during the transition from the third to the fourth months. However, the composition of T4 underwent modifications between any two consecutive months. Consequently, the correct answer is (1, 0).

Answer 2

Given that 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, … till T5, 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 presents 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 illustrates 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 illustrates 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.
 

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

From option b, the transfer of one SE from T1 to T5 is required. However, since there are no SEs in T1, this transfer cannot occur. Additionally, one SE must be transferred from T2 to T4, and one RE must be transferred from T4 to T2. Nevertheless, since there are no REs in T4, this transfer is not feasible. Therefore, these specific transfers do not take place.

The subsequent table outlines the employee count for each team in the fourth month. In the fifth month, the challenging project is assigned to T5. As per option a, two SEs are moved from T4 to T5, and one RE is relocated from T5 to T4. Despite the requirement for one SE to be transferred from T1 to T5 according to option b, this action cannot be executed due to the absence of SEs in T1. Additionally, one SE will be transferred from T2 to T4, and one RE will be transferred from T4 to T2.

The following table illustrates the number of employees in each team for 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

The count of SEs in T1 during the third month is 0, while the number of SEs in T5 during the third month is 2. Therefore, the correct answer is (0, 2).

Answer 3

Given that 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, … till T5, 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 presents 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 illustrates 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 illustrates 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.
 

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

From option b, the transfer of one SE from T1 to T5 is required. However, since there are no SEs in T1, this transfer cannot occur. Additionally, one SE must be transferred from T2 to T4, and one RE must be transferred from T4 to T2. Nevertheless, since there are no REs in T4, this transfer is not feasible. Therefore, these specific transfers do not take place.

The subsequent table outlines the employee count for each team in the fourth month. In the fifth month, the challenging project is assigned to T5. As per option a, two SEs are moved from T4 to T5, and one RE is relocated from T5 to T4. Despite the requirement for one SE to be transferred from T1 to T5 according to option b, this action cannot be executed due to the absence of SEs in T1. Additionally, one SE will be transferred from T2 to T4, and one RE will be transferred from T4 to T2.

The following table illustrates the number of employees in each team for 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

Considering that challenging projects have 200 credits and standard projects have 100 credits, each employee's credits are shared equally within the team for each type of project. Therefore, for a challenging project, an employee earns \(\frac{200}{5} = 40\) credits, and for a standard project, an employee earns \(\frac{100}{4} = 25\) credits.
Over the course of five months, an employee can work on different combinations of challenging and standard projects. The possible scenarios include working on five challenging projects, four challenging projects and one standard project, three challenging projects and two standard projects, two challenging projects and three standard projects, one challenging project and four standard projects, or five standard projects.
In each case, an employee will earn a total of 200, 185, 170, 155, 140, or 125 credits. 
Therefore, it is not possible for an employee to earn exactly 150 credits based on the given project types and credit distribution.

Answer 4

Given that 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, … till T5, 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 presents 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 illustrates 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 illustrates 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.
 

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

From option b, the transfer of one SE from T1 to T5 is required. However, since there are no SEs in T1, this transfer cannot occur. Additionally, one SE must be transferred from T2 to T4, and one RE must be transferred from T4 to T2. Nevertheless, since there are no REs in T4, this transfer is not feasible. Therefore, these specific transfers do not take place.

The subsequent table outlines the employee count for each team in the fourth month. In the fifth month, the challenging project is assigned to T5. As per option a, two SEs are moved from T4 to T5, and one RE is relocated from T5 to T4. Despite the requirement for one SE to be transferred from T1 to T5 according to option b, this action cannot be executed due to the absence of SEs in T1. Additionally, one SE will be transferred from T2 to T4, and one RE will be transferred from T4 to T2.

The following table illustrates the number of employees in each team for 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

Since Aneek secured 185 credits, he worked in four challenging projects and one standard project. Let's analyze the options:
Option A: Aneek could have worked in T1 in the first month (challenging project), T2 in the second month (challenging project), T3 in the third month (challenging project), T4 in the fourth month (challenging project), and T5 in the fifth month (standard project). Hence, this is possible.
Option B: Aneek could have worked in T1 in the first month (challenging project), T2 in the second month (challenging project), T4 in the third month (standard project), T4 in the fourth month (challenging project), and T5 in the fifth month (challenging project). Hence, this is possible.
Option C: Aneek could have worked in T2 in the first month (standard project), T2 in the second month (challenging project), T3 in the third month (challenging project), T4 in the fourth month (challenging project), and T5 in the fifth month (challenging project). Hence, this is possible.
Option D: Aneek could have worked in T1 in the first month (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.

Therefore, option D is the correct choice.