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 T5 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.
Which of the following CANNOT be the total credit points earned by any employee from the projects?
Correct Answer :
150
Solution :
The correct option is B.
Let's calculate the points earned by an employee in each month:
- A standard project has 100 credit points and is completed by a team of 4 employees. Therefore, each employee in a standard project earns:
points.
- A challenging project has 200 credit points and is completed by a team of 5 employees. Therefore, each employee in a challenging project earns:
points.
Let c be the number of challenging projects an employee works on during the 5 months (where 0 ≤ c ≤ 5). The remaining (5 - c) projects will be standard projects. The total credit points earned by the employee will be:
Total = 40c + 25(5 - c) = 125 + 15c
Substituting possible values for c:
- For c = 0: Total = 125 + 15(0) = 125 points
- For c = 1: Total = 125 + 15(1) = 140 points
- For c = 2: Total = 125 + 15(2) = 155 points
- For c = 3: Total = 125 + 15(3) = 170 points
- For c = 4: Total = 125 + 15(4) = 185 points
- For c = 5: Total = 125 + 15(5) = 200 points
From the options, 150 is not a possible score. Thus, 150 cannot be the total credit points earned by any employee.
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