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 T 4 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.
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:
- (2, 1)
- (1, 0)
- (0, 0)
- (1, 1)
The Correct Option is B
Solution and Explanation
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).
The number of SE in T1 and T5 for the projects in the third month are, respectively:
- (0, 2)
- (0, 3)
- (1, 2)
- (1, 3)
The Correct Option is A
Solution and Explanation
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).
Which of the following CANNOT be the total credit points earned by any employee from the projects?
- 140
- 150
- 170
- 200
The Correct Option is B
Solution and Explanation
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.
One of the employees named Aneek scored 185 points. Which of the following CANNOT be true?
- Aneek worked only in teams T1, T2, T3, and T4
- Aneek worked only in teams T1, T2, T4, and T5
- Aneek worked only in teams T2, T3, T4, and T5
- Aneek worked only in teams T1, T3, T4, and T5
The Correct Option is D
Solution and Explanation
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.
Top Questions on Data Analysis
- The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections. Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs.
The following additional information is known.
The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.
The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.
- The two plots below give the following information about six firms A, B, C, D, E, and F for 2019 and 2023.
PAT: The firm’s profits after taxes in Rs. crores,
ES: The firm’s employee strength, that is the number of employees in the firm, and PRD: The percentage of the firm’s PAT that they spend on Research and Development (R&D).
In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the two years.
- The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row. - Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
7. Player-4's rating was double of Player-8's and less than Player-5's. - The chart below shows the price data for seven shares – A, B, C, D, E, F, and G as a candlestick plot for a particular day. The vertical axis shows the price of the share in rupees. A share whose closing price (price at the end of the day) is more than its opening price (price at the start of the day) is called a bullish share; otherwise, it is called a bearish share. All bullish and bearish shares are shown in green and red colour respectively.
Questions Asked in CAT exam
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Time and Work
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Time and Work
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems