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Test Level 3: Caselets - 2 - CAT MCQ


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20 Questions MCQ Test Level-wise Tests for CAT - Test Level 3: Caselets - 2

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Test Level 3: Caselets - 2 - Question 1

Directions: Refer to the data below and answer the question that follows.

The table below gives the number of times 8 colleges viz. P, Q, R, S, T, U, V and W won gold, silver or bronze medals and obtained 4th, 5th and 6th places in intercollege competitions held this year.

The number of points the college scored during the competitions is calculated using the following formula:
Number of points = (Gold medals) × 3 + (Silver medals) × 2 + (Bronze medals) +[(1 - 0.1 × place) × (places)
[Note: (places) or (medals) refers to the number of times the college won that place or that medal]
Some additional facts that are known are as follows:
(i) The number of bronze medals won by college P is the same as the number of silver medals won by college Q.
(ii) The number of times college U was at the 4th place is the same as the number of bronze medals won by college T.
(iii) No two colleges are assigned the same place in a game.

Q. If 7th and 8th places are also assigned, then which college won these places the minimum number of times?

Detailed Solution for Test Level 3: Caselets - 2 - Question 1

Since the total number of gold medals won is 36, the total number of games played should be 36, i.e. total number of silver medals, bronze medals and the places must be 36.
Therefore, silver medals won by college Q = 36 – (5 + 4 + 8 + 3 + 7 + 2 + 1) = 36 – 30 = 6
Then, from (i), bronze medals won by college P = 6
Number of times college U won the 4th place = 36 – (0 + 4 + 5 + 8 + 8 + 4 + 4) = 36 – 33 = 3
Then, from (ii), bronze medals won by college T = 3
So, bronze medals won by college S = 36 – (6 + 3 + 2 + 3 + 10 + 5 + 5) = 36 – 34 = 2
Let college R win the 5th place x times and the 6th place y times and school U win the 5th place z times and the 6th place w times. Then, we get
x + z = 3, y + w = 14 and 0.5x + 0.4y = 4.4
i.e. x + z = 3, 5x + 4y = 44
Now, consider the cases for x + z = 3
For all other values of x (i.e. 1, 2, 3), we do not get integer values for y and w.
So, x = 0, y = 11, w = 3 and z = 3.
We know that every college played 36 games. Therefore, the total number of medals and places won by each college must add up to 36.
Therefore, the number of 7th and 8th places won by the college = 36 – (gold, silver, bronze, 4th, 5th, 6th places won by the college)
Hence, we can complete the table as follows:

College T won 7th and 8th places the minimum number of times, i.e. 5.

Test Level 3: Caselets - 2 - Question 2

Directions: Refer to the data below and answer the question that follows.

The table below gives the number of times 8 colleges viz. P, Q, R, S, T, U, V and W won gold, silver or bronze medals and obtained 4th, 5th and 6th places in intercollege competitions held this year.

The number of points the college scored during the competitions is calculated using the following formula:
Number of points = (Gold medals) × 3 + (Silver medals) × 2 + (Bronze medals) +[(1 - 0.1 × place) × (places)
[Note: (places) or (medals) refers to the number of times the college won that place or that medal]
Some additional facts that are known are as follows:
(i) The number of bronze medals won by college P is the same as the number of silver medals won by college Q.
(ii) The number of times college U was at the 4th place is the same as the number of bronze medals won by college T.
(iii) No two colleges are assigned the same place in a game.

Q. How many times did college U win the 5th place?

Detailed Solution for Test Level 3: Caselets - 2 - Question 2

Since the total number of gold medals won is 36, the total number of games played should be 36, i.e. total number of silver medals, bronze medals and the places must be 36.
Therefore, silver medals won by college Q = 36 – (5 + 4 + 8 + 3 + 7 + 2 + 1) = 36 – 30 = 6
Then, from (i), bronze medals won by college P = 6
Number of times college U won the 4th place = 36 – (0 + 4 + 5 + 8 + 8 + 4 + 4) = 36 – 33 = 3
Then, from (ii), bronze medals won by college T = 3
So, bronze medals won by college S = 36 – (6 + 3 + 2 + 3 + 10 + 5 + 5) = 36 – 34 = 2
Let college R win the 5th place x times and the 6th place y times and school U win the 5th place z times and the 6th place w times. Then, we get
x + z = 3, y + w = 14 and 0.5x + 0.4y = 4.4
i.e. x + z = 3, 5x + 4y = 44
Now, consider the cases for x + z = 3
For all other values of x (i.e. 1, 2, 3), we do not get integer values for y and w.
So, x = 0, y = 11, w = 3 and z = 3.
We know that every college played 36 games. Therefore, the total number of medals and places won by each college must add up to 36.
Therefore, the number of 7th and 8th places won by the college = 36 – (gold, silver, bronze, 4th, 5th, 6th places won by the college)
Hence, we can complete the table as follows:

Number of times college U won the 5th place = 3

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Test Level 3: Caselets - 2 - Question 3

Directions: Refer to the data below and answer the question that follows:
The daily demand (in number of customers) for air travel from Delhi to Bangalore and from Bangalore to Delhi, each is 1200 customers. The breakdown of demand by time is given in the following table:

The demand for travel from Bangalore to Delhi is identical to that from Delhi to Bangalore. Any unmet demand in any time period does not spill over to the next time period.
Space jet, an airline, which flies only between Delhi and Bangalore has the following costs:
1. A surcharge A per passenger of Rs. 100 to be paid to the Airlines Regulatory Board.
2. A fixed cost B of Rs. 72000 per trip made.
The airline owns 2 planes, each with a maximum capacity of 150 passengers. One plane is parked at Delhi and the other at Bangalore at the beginning of the day. One trip (from Delhi to Bangalore or vice versa) takes 1.5 hours. The airline charges a uniform fare of Rs. 1000 per passenger per trip.

Customer satisfaction index (CSI) is defined as: 

CSI = 1 - (Unmet demand)/(Total number of passengers that the airline carries on that day)

Q. Consider the definition of CSI. If the airline wishes to achieve a CSI of 1.00 by purchasing another smaller aircraft while making no losses on the smaller aircraft, what is/are the possible cost structure(s) for the smaller aircraft? Assume that there are only surcharge costs per passenger and a fixed cost per trip while the fare per passenger is the same.

Detailed Solution for Test Level 3: Caselets - 2 - Question 3

The implication of unmet demand not spilling over is equivalent to each time period's demand, independent of all other time periods. Hence, the maximum profit is obtained when the number of profitable passengers is maximised for each time period. More than 80 passengers are needed for a profitable trip as for 80 passengers, the fare is Rs. 80000 and the cost is Rs. 72000 + Rs. 8000 = Rs. 80000. For each additional passenger over and above 80 passengers in a trip, the airline makes a profit of Rs. 1000 – Rs. 100 = Rs. 900.
Note that all the demand is now at the beginning of the time period. In a 2 hours and 59 minutes span, a plane can start a maximum of two trips since it takes 1.5 hours for a trip. Consider the first time period: 6 am - 8:59 am. Since there 360 passengers waiting for the trip, starting at 6 am, at each destination, the airline can make two trips (of each plane) with the maximum capacity of 150 passengers at a time from Delhi to Bangalore and Bangalore to Delhi. Similarly, a plane at Bangalore will carry 150 passengers at a time from Bangalore to Delhi and Delhi to Bangalore. Consider the time period 9 am - 11:59 am. Since there are 240 passengers waiting for the trip at each destination, two trips (of each plane) cannot be made with 150 passengers and another with 90 passengers or 2 trips with 120 passengers in each trip.

Applying similar arguments to each time period, we obtain the following table for trips from Delhi to Bangalore to maximise the profit:

In order to achieve a CSI of 1.00, there should be no unmet demand in any time period.
From the table given above, it is implied that the smaller aircraft will need to make 2 trips, one trip with 60 people in the first time period and one trip with 30 people between 3 and 5:59 pm.
Hence, the smaller aircraft should be profitable with 30 people, i.e. 30 x A + F ≤ 30 x 1000, where A is the surcharge per passenger and F is the fixed cost per trip.
Plugging in the values of A and F in the given options, option 4 is the only possible answer.

Test Level 3: Caselets - 2 - Question 4

Directions: Refer to the data below and answer the question that follows:
The daily demand (in number of customers) for air travel from Delhi to Bangalore and from Bangalore to Delhi, each is 1200 customers. The breakdown of demand by time is given in the following table:

The demand for travel from Bangalore to Delhi is identical to that from Delhi to Bangalore. Any unmet demand in any time period does not spill over to the next time period.
Space jet, an airline, which flies only between Delhi and Bangalore has the following costs:
1. A surcharge A per passenger of Rs. 100 to be paid to the Airlines Regulatory Board.
2. A fixed cost B of Rs. 72000 per trip made.
The airline owns 2 planes, each with a maximum capacity of 150 passengers. One plane is parked at Delhi and the other at Bangalore at the beginning of the day. One trip (from Delhi to Bangalore or vice versa) takes 1.5 hours. The airline charges a uniform fare of Rs. 1000 per passenger per trip.

Customer satisfaction index (CSI) is defined as: 

CSI = 1 - (Unmet demand)/(Total number of passengers that the airline carries on that day)

Q. What is the CSI for the airline in a day?

Detailed Solution for Test Level 3: Caselets - 2 - Question 4

The implication of unmet demand not spilling over is equivalent to each time period's demand, independent of all other time periods. Hence, the maximum profit is obtained when the number of profitable passengers is maximised for each time period. More than 80 passengers are needed for a profitable trip as for 80 passengers, the fare is Rs. 80000 and the cost is Rs. 72000 + Rs. 8000 = Rs. 80000. For each additional passenger over and above 80 passengers in a trip, the airline makes a profit of Rs. 1000 – Rs. 100 = Rs. 900.
Note that all the demand is now at the beginning of the time period. In a 2 hours and 59 minutes span, a plane can start a maximum of two trips since it takes 1.5 hours for a trip. Consider the first time period: 6 am - 8:59 am. Since there 360 passengers waiting for the trip, starting at 6 am, at each destination, the airline can make two trips (of each plane) with the maximum capacity of 150 passengers at a time from Delhi to Bangalore and Bangalore to Delhi. Similarly, a plane at Bangalore will carry 150 passengers at a time from Bangalore to Delhi and Delhi to Bangalore. Consider the time period 9 am - 11:59 am. Since there are 240 passengers waiting for the trip at each destination, two trips (of each plane) cannot be made with 150 passengers and another with 90 passengers or 2 trips with 120 passengers in each trip.

Applying similar arguments to each time period, we obtain the following table for trips from Delhi to Bangalore to maximise the profit:

From the table, unmet demand = 90 and total number of people who travel = 1200 – 90 = 1110.
Therefore, CSI = 1 - [90/1110] = 0.9189 = 0.92 (approx.)

Test Level 3: Caselets - 2 - Question 5

Directions: Answer the question on the basis of the information given below.
The following table provides information about the marks obtained by following sixteen students in Quantitative Aptitude, Logical Reasoning and Data Interpretation and Verbal Ability in an MBA entrance test for an MBA Institute.
(i) The total marks obtained by the student in the test is the sum of the marks obtained by the student in the mentioned three sections. It also provides information about the centre at which the student is enroled.
(ii) The students belong to either one of the three centres namely Jaipur, Delhi and Punjab. Each student is enroled at only one centre.
(iii) Each student is given only one rank from 1 to 16 based on the marks obtained by him/her in the entrance test. This rank is called 'overall rank'.
Note: 
A student A (assume) is given a numerically lesser rank than the other student B (assume) if the total marks obtained by A is greater than the total marks obtained by B.

  • If the total marks obtained by A is same as those obtained by B, then the student having obtained more marks in Verbal Ability section is given a numerically lesser rank.
  • If marks obtained by two students in Verbal Ability section are also same, then the student having obtained more marks in Logical Reasoning and Data Interpretation section is given a numerically lesser rank.

Q. Name the person whose rank is between the ranks of Aarti and Prakash.

Detailed Solution for Test Level 3: Caselets - 2 - Question 5

The total marks obtained by the students and their overall ranks are tabulated in the following table:

Rank of Aarti is 9 and that of Prakash is 11.
Thus, Nidhi, who has got rank 10 is between the ranks of Aarti and Prakash.

Test Level 3: Caselets - 2 - Question 6

Directions: Answer the question on the basis of the information given below.
The following table provides information about the marks obtained by following sixteen students in Quantitative Aptitude, Logical Reasoning and Data Interpretation and Verbal Ability in an MBA entrance test for an MBA Institute.
(i) The total marks obtained by the student in the test is the sum of the marks obtained by the student in the mentioned three sections. It also provides information about the centre at which the student is enroled.
(ii) The students belong to either one of the three centres namely Jaipur, Delhi and Punjab. Each student is enroled at only one centre.
(iii) Each student is given only one rank from 1 to 16 based on the marks obtained by him/her in the entrance test. This rank is called 'overall rank'.
Note: 
A student A (assume) is given a numerically lesser rank than the other student B (assume) if the total marks obtained by A is greater than the total marks obtained by B.

  • If the total marks obtained by A is same as those obtained by B, then the student having obtained more marks in Verbal Ability section is given a numerically lesser rank.
  • If marks obtained by two students in Verbal Ability section are also same, then the student having obtained more marks in Logical Reasoning and Data Interpretation section is given a numerically lesser rank.

Q. Find the rank of Deepika.

Detailed Solution for Test Level 3: Caselets - 2 - Question 6

The total marks obtained by the students and their overall ranks are tabulated in the following table:

Thus, the rank of Deepika is 13.

Test Level 3: Caselets - 2 - Question 7

Directions: Answer the following question based on the information given below.
Tina, a blast furnace expert, who works as a technology trouble shooter stays in Jamshedpur. She has got an important assignment in Delhi, which requires 6 hours to complete. The work is so critical that she has to start working the moment she reaches the client's premises.
She is considering various options for her onward and return journey between Jamshedpur and Delhi.
A quick search revealed that ticket from Jamshedpur to Delhi is available on 2 trains. Trains 12801 and 12443 depart from Jamshedpur station at 06:45 hrs and 15:55 hrs and reach Delhi next day at 04:50 hrs and 10:35 hrs, respectively. Trains 12444 and 12802 start from Delhi at 17:20 hrs and 22:20 hrs and reach Jamshedpur next day at 10:35 hrs and 20:05 hrs, respectively.
Another option is to reach Ranchi by a 3-hour road trip and take a flight to Delhi from Ranchi. The distance between Delhi and Ranchi is covered in 105 minutes both ways by any of the scheduled flights. Air India operates 2 flights AI 9810 and AI 810, which depart Ranchi at 08:00 hours and 15:25 hrs, respectively. Flight number IT - 3348 operated by Kingfisher Airlines departs Ranchi at 19:20 hrs. Return flights operated by Air India - AI 9809 and AI809 depart Delhi at 05:50 hrs and 11:00 hrs, respectively. Flight number IT - 3347 operated by Kingfisher Airlines departs Delhi at 17:10 hrs.
From Tina's home, Jamshedpur railway station is 5 minutes drive, and her destination at Delhi is 90 minutes and 30 minutes drive from airport and railway station, respectively. One has to reach the airport at least 1 hour before the scheduled departure to complete the boarding procedure. At every railway station, she loses 5 minutes in navigating through the crowd.

Q. Tina appeared for an exam on 8th of January in Jamshedpur and then she started from her residence in Jamshedpur only after 16:00 hrs of the same day. Choose the option, from the ones given below, that will help her to minimise the total time out of Jamshedpur.

Detailed Solution for Test Level 3: Caselets - 2 - Question 7

Let us evaluate this option wise.
Let us consider option 1. Option 1 states that she boards train 12443.
But train 12443 departs at 15:55 and there is no way she can catch it.
This option is thus ruled out.
Let us now evaluate option 2.
Option 2 again asks to board train 12443, which is not feasible.
Thus, option 2 too is ruled out.
Let us now evaluate option 3.
Option 3 suggests that she goes by IT 3348 and returns by train 12801.
In order to catch IT 3348, which departs from Ranchi airport at 19:20, she has to start off from her home latest by 15:20, which is not feasible as she cannot leave before 16:00.
Thus, this option is ruled out as well.
Let us now evaluate option 4.
So, to board AI 9810 at 08:00 the next day, she has to leave for Ranchi at 04:00.
She reaches Delhi at 09:45 and then reaches the client's site at 11:15, where she works till 17:15.
Next morning she catches AI 9809 at 05:50 and reaches Ranchi at 07:35 and finally Jamshedpur at 10:35.
Thus, she is away from Jamshedpur for 30 hours and 35 minutes.
As option 4 is the only logically possible option, so option 4 is correct.

Test Level 3: Caselets - 2 - Question 8

Directions: Answer the following question based on the information given below.
Tina, a blast furnace expert, who works as a technology trouble shooter stays in Jamshedpur. She has got an important assignment in Delhi, which requires 6 hours to complete. The work is so critical that she has to start working the moment she reaches the client's premises.
She is considering various options for her onward and return journey between Jamshedpur and Delhi.
A quick search revealed that ticket from Jamshedpur to Delhi is available on 2 trains. Trains 12801 and 12443 depart from Jamshedpur station at 06:45 hrs and 15:55 hrs and reach Delhi next day at 04:50 hrs and 10:35 hrs, respectively. Trains 12444 and 12802 start from Delhi at 17:20 hrs and 22:20 hrs and reach Jamshedpur next day at 10:35 hrs and 20:05 hrs, respectively.
Another option is to reach Ranchi by a 3-hour road trip and take a flight to Delhi from Ranchi. The distance between Delhi and Ranchi is covered in 105 minutes both ways by any of the scheduled flights. Air India operates 2 flights AI 9810 and AI 810, which depart Ranchi at 08:00 hours and 15:25 hrs, respectively. Flight number IT - 3348 operated by Kingfisher Airlines departs Ranchi at 19:20 hrs. Return flights operated by Air India - AI 9809 and AI809 depart Delhi at 05:50 hrs and 11:00 hrs, respectively. Flight number IT - 3347 operated by Kingfisher Airlines departs Delhi at 17:10 hrs.
From Tina's home, Jamshedpur railway station is 5 minutes drive, and her destination at Delhi is 90 minutes and 30 minutes drive from airport and railway station, respectively. One has to reach the airport at least 1 hour before the scheduled departure to complete the boarding procedure. At every railway station, she loses 5 minutes in navigating through the crowd.

Q. If Tina wants to spend the minimum time out of Jamshedpur, the best option for her from among the following is to go by:

Detailed Solution for Test Level 3: Caselets - 2 - Question 8

Let us evaluate this option wise.
Firstly, let us evaluate option 1.
She departs Jamshedpur for Ranchi airport at 04:00.
Flight departure time = 08:00
Flight arrival time in Delhi = 09:45
She reaches client's site at 11:15
She completes work by 17:15.
Reaches Delhi airport by 18:45
So, she won't be able to catch the flight.
This option is thus ruled out.
Let us now evaluate option 2.
She departs Jamshedpur for Ranchi airport at 04:00.
Flight departure time = 08:00
Flight arrival time in Delhi = 09:45
She reaches the client's site at 11:15.
She completes the work by 17:15.
She will reach the station by 17:45 and be able to board the train by 17:50.
Thus, she will have to wait for another 4.5 hours before the train departs for Jamshedpur at 22:20.
Time the train reaches Jamshedpur = 20:05 the next day
So, total time she is away from Jamshedpur = 4:00 a.m. to 20:05 the next day = 40 hr 5 min
Let us now evaluate option 3.
She leaves Jamshedpur for Ranchi airport at 15:20.
She departs for Delhi from Ranchi via flight IT 3348 at 19:20 and reaches Delhi at 21:05.
She then reaches the client's site at 22:35 and gets free from there at 04:35.
She reaches Delhi airport at 05:05 and does not have sufficient time to board AI 9809.
This option is thus ruled out.
Let us now evaluate option 4.
She departs from Jamshedpur railway station for Delhi at 15:55 hrs and reaches Delhi the next day at 10:35 hrs.
She departs the railway station for the client's site at 10:40 and reaches there at 11:10.
She gets free from there at 17:10 and reaches back at station at 17:40 where she can board the train by 17:45.
But, train 12444 has already departed by then.
Thus, this option too is ruled out.
Thus, the only feasible option is option 2 for which she is away from Jamshedpur for a period of 40 hours and 5 minutes.
Hence, answer option 2 is correct.

Test Level 3: Caselets - 2 - Question 9

Directions: Read the information carefully to answer the question that follows.
Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.
Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.
It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.

Q. What is the ratio of total number of students who performed below average and number of students who performed above average in classes P, S and T?

Detailed Solution for Test Level 3: Caselets - 2 - Question 9

Number of students in class 1 = 20
Number of students in class 3 = 40
Number of students in class 9 = 80
Number of students in class 10 = 60
Number of students in class 2 = 85
Number of students in class 6 = 50
Number of students in class 7 = 30
Let the number of students in class 4 = x
Number of students in class 5 = 3x
Number of students in class 8 = 1.4x
Also,
x + 1.4x + 3x = 135
x = 25
Number of students in class 4 = 25
Number of students in class 5 = 75
Number of students in class 8 = 35
So, total students = 20 + 40 + 80 + 60 + 85 + 50 + 30 + 135 = 500
Number of students in class R = 100
Number of students in class Q = 0.23 × 500 = 115
Number of students in class T = 0.17 × 500 = 85
Remaining students = 200
Number of students in class P = 11 × 200/20 = 110
Number of students in class S = 200 - 110 = 90
Since each of classes P, Q, R, S and T is divided into two parts, so possible choices are
For 85, its
(50, 35) and (60, 25)
For 90, its
(60, 30) and (50, 40)
Similarly, for 100 as sum, 3 cases are possible and for 110 as sum, 4 cases are possible.
It is also mentioned that in each class, the ratio of below average and above average performers is at least 13/10.
So, following table can be formed from given information after considering ratio case.
Class S is divided into class 7 (above average students) and 10 (below average students)
Class T is divided into class 6 (below average students) and class 8 (above average students)
Class R is divided into class 1 (above average students) and class 9 (below average students)
Class P is divided into class 4 (above average students) and class 2 (below average students)
Class Q is divided into class 3 (above average students) and class 5 (below average students)
Required ratio = (85 + 60 + 50)/(25 + 30 + 35) = 13 : 6

Test Level 3: Caselets - 2 - Question 10

Directions: Read the information carefully to answer the question that follows.
Dr. Ravi Patel teaches financial markets course at Indian Management Institute, which is being taught in two parts - one part in first trimester and the other part in second trimester. Initially, the professor divides the students randomly in five classes in first trimester and based on the performance of students in first trimester, he further divides the students of each class into two parts as below average and above average performers. It is observed that in each class, the ratio of below average and above average performers is at least 13/10.
Initially, the classes were named as classes P, Q, R, S and T and after further division, the classes were renamed as classes 1, 2, 3, 4 ,....,10 and the classes in trimester 2 are named randomly i.e. it is not necessary that two parts of class A are numbered one after the other.
It is also given that 1/5 of total students in first trimester were in class R, 23% of total students were in class Q and 17% of total students were in class T. The ratio of students in classes P and S was 11 : 9. In the second trimester, there were 20 students in class 1. The number of students in classes 3, 10 and 9 were twice, thrice and four times the number of students in class 1. The number of students in classes 4 and 5 are in ratio 1 : 3. The number of students in class 2 were 5 more than the number of students in class 9. The number of students in class 8 was 40% more than the number of students in class 4. The number of students in classes 6 and 7 is 50 and 30 and the total number of students in classes 4, 5 and 8 is 125% more than the number of students in class 10. Each student in first trimester was classified as either below average or above average performer.

Q. What was the minimum difference between number of students who performed below average and number of students who performed above average in any class?

Detailed Solution for Test Level 3: Caselets - 2 - Question 10

Number of students in class 1 = 20
Number of students in class 3 = 40
Number of students in class 9 = 80
Number of students in class 10 = 60
Number of students in class 2 = 85
Number of students in class 6 = 50
Number of students in class 7 = 30
Let the number of students in class 4 = x
Number of students in class 5 = 3x
Number of students in class 8 = 1.4x
Also,
x + 1.4x + 3x = 135
x = 25
Number of students in class 4 = 25
Number of students in class 5 = 75
Number of students in class 8 = 35
So, total students = 20 + 40 + 80 + 60 + 85 + 50 + 30 + 135 = 500
Number of students in class R = 100
Number of students in class Q = 0.23 × 500 = 115
Number of students in class T = 0.17 × 500 = 85
Remaining students = 200
Number of students in class P = 11 × 200/20 = 110
Number of students in class S = 200 - 110 = 90
Since each of classes P, Q, R, S and T is divided into two parts, so possible choices are
For 85, its
(50, 35) and (60, 25)
For 90, its
(60, 30) and (50, 40)
Similarly, for 100 as sum, 3 cases are possible and for 110 as sum, 4 cases are possible.
It is also mentioned that in each class, the ratio of below average and above average performers is at least 13/10.
So, following table can be formed from given information after considering ratio case.
Class S is divided into class 7 (above average students) and 10 (below average students)
Class T is divided into class 6 (below average students) and class 8 (above average students)
Class R is divided into class 1 (above average students) and class 9 (below average students)
Class P is divided into class 4 (above average students) and class 2 (below average students)
Class Q is divided into class 3 (above average students) and class 5 (below average students)
Minimum difference between number of students who performed below average and number of students who performed above average in any class was 15 in class T.

Test Level 3: Caselets - 2 - Question 11

Mr Ahluwalia, Mr Bhatia, Mr Chopra, Mr Dayal, and Mr. Eeshwar have first and middle names as per the following conditions: (Each of them has different first and middle names).
(i) Four of them have a first or middle name of Ram, three of them have first or middle name of Shyam, two of them have a first or middle name of Tram and one of them has a first or middle name of Alam. 
(ii) Either Mr Ahluwalia and Mr Bhatia are both named Tram or Mr Chopra and Mr Dayal are both named Tram. 
(iii) Of Mr Bhatia and Mr Chopra either both are named Shyam or neither is named Shyam. 
(iv) Mr Dayal and Mr Eeshwar are both not named Ram.

Q. Which of these is a possible combination of names?

Detailed Solution for Test Level 3: Caselets - 2 - Question 11

Hence, None of the 3 name combination appears.

Test Level 3: Caselets - 2 - Question 12

Mr Ahluwalia, Mr Bhatia, Mr Chopra, Mr Dayal, and Mr. Eeshwar have first and middle names as per the following conditions: (Each of them has different first and middle names).
(i) Four of them have a first or middle name of Ram, three of them have first or middle name of Shyam, two of them have a first or middle name of Tram and one of them has a first or middle name of Alam. 
(ii) Either Mr Ahluwalia and Mr Bhatia are both named Tram or Mr Chopra and Mr Dayal are both named Tram. 
(iii) Of Mr Bhatia and Mr Chopra either both are named Shyam or neither is named Shyam. 
(iv) Mr Dayal and Mr Eeshwar are both not named Ram.

Q. Who is named Alam?

Detailed Solution for Test Level 3: Caselets - 2 - Question 12

Hence Mr. Bhatia is the correct option.

Test Level 3: Caselets - 2 - Question 13

Mr Ahluwalia, Mr Bhatia, Mr Chopra, Mr Dayal, and Mr. Eeshwar have first and middle names as per the following conditions: (Each of them has different first and middle names).
(i) Four of them have a first or middle name of Ram, three of them have first or middle name of Shyam, two of them have a first or middle name of Tram and one of them has a first or middle name of Alam. 
(ii) Either Mr Ahluwalia and Mr Bhatia are both named Tram or Mr Chopra and Mr Dayal are both named Tram. 
(iii) Of Mr Bhatia and Mr Chopra either both are named Shyam or neither is named Shyam. 
(iv) Mr Dayal and Mr Eeshwar are both not named Ram.

Q. Which of these people have the same name?

Detailed Solution for Test Level 3: Caselets - 2 - Question 13

Mr. Ahluwalia and Mr. Eeshwar are both named Ram Shyam. Hence option  c is correct.

Test Level 3: Caselets - 2 - Question 14

Mr Ahluwalia, Mr Bhatia, Mr Chopra, Mr Dayal, and Mr. Eeshwar have first and middle names as per the following conditions: (Each of them has different first and middle names).(i) Four of them have a first or middle name of Ram, three of them have first or middle name of Shyam, two of them have a first or middle name of Tram and one of them has a first or middle name of Alam. (ii) Either Mr Ahluwalia and Mr Bhatia are both named Tram or Mr Chopra and Mr Dayal are both named Tram. (iii) Of Mr Bhatia and Mr Chopra either both are named Shyam or neither is named Shyam. (iv) Mr Dayal and Mr Eeshwar are both not named Ram.

Q. The two Trams are:

Detailed Solution for Test Level 3: Caselets - 2 - Question 14

Finally The two Trams are Chopra and Dayal, Hence b is the correct answer

Test Level 3: Caselets - 2 - Question 15

Mr Ahluwalia, Mr Bhatia, Mr Chopra, Mr Dayal, and Mr. Eeshwar have first and middle names as per the following conditions: (Each of them has different first and middle names).(i) Four of them have a first or middle name of Ram, three of them have first or middle name of Shyam, two of them have a first or middle name of Tram and one of them has a first or middle name of Alam. (ii) Either Mr Ahluwalia and Mr Bhatia are both named Tram or Mr Chopra and Mr Dayal are both named Tram. (iii) Of Mr Bhatia and Mr Chopra either both are named Shyam or neither is named Shyam. (iv) Mr Dayal and Mr Eeshwar are both not named Ram.

Q. Mr Eeshwar is known as:

Detailed Solution for Test Level 3: Caselets - 2 - Question 15

Hence, Mr Eeshwar is is Ram Shyam.

Test Level 3: Caselets - 2 - Question 16

Directions: Re ad the following case let and choose the best alternative.

Mr. Rajiv Singhal, Chairman of the Board of Directors of Loha India Ltd., (a steel manufacturing company) had just been visited by several other directors of the company.
The directors were upset with recent actions of the company president, Mr. Ganesh Thakur. They demanded that the board consider firing the president.
Mr. Thakur, recently appointed as president, had undertaken to solve some of the management-employees problems by dealing directly with the individuals, as often as possible. The company did not have a history of strikes or any other form of collective action and was considered to have a good work culture. However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees. An important initiative of Mr. Thakur was to negotiate wages of the supervisors with each supervisor. In these negotiation meetings he would not involve anyone else, including the Personnel Department which reported to him, so as to take an unbiased decision. After negotiation, a wage contract would be drawn up for each supervisor. This, he felt, would recognise and reward the better performers. Mr. Thakur successfully implemented the process for most of the supervisors, except those working in the night shift. For them he had drawn up the contracts unilaterally benchmarking the wages of supervisors of night shift with that of supervisors of the day shift.
For several days Ram Lal a night shift supervisor, had been trying to seek an appointment with Mr. Thakur about his wages. He was disgruntled, not only over his failure to see the president, but also over the lack of discussions about his wage contract prior to its being effected. As a family man with six dependents, he felt his weekly wage should be higher than that granted to him.
Last Thursday afternoon Ram Lal stopped by the president’s office and tried to see him.
Mr. Thakur ’s secretary refused his request on the grounds that Mr. Thakur was busy.
Infuriated, Ram Lal stormed into the president’s office and confronted the startled Mr.
Thakur, with his demands for a better wage. Mr. Thakur stood up and told Ram Lal to get out of his office and express his grievance through official channel. Ram Lal took a swing at the president who in turn punched Ram Lal on the jaw and knocked him unconscious.

Q. The most likely premise behind Mr. Thakur ’s initiative regarding individualised meetings with the supervisors seems to be

Detailed Solution for Test Level 3: Caselets - 2 - Question 16

From what is given in the caselet, it is evident that option (a) can be inferred.
The premise that the involvement of the company’s president in wage problems of employees would lead to a better goodwill towards the management among the workers. This is clearly inferable from the third sentence in the second paragraph of the passage which states: “However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees.”.
Each of the other options can be easily rejected based on an understanding of the central theme of the situation.
Hence, option (a) is correct.

Test Level 3: Caselets - 2 - Question 17

Directions: Re ad the following case let and choose the best alternative.

Mr. Rajiv Singhal, Chairman of the Board of Directors of Loha India Ltd., (a steel manufacturing company) had just been visited by several other directors of the company.
The directors were upset with recent actions of the company president, Mr. Ganesh Thakur. They demanded that the board consider firing the president.
Mr. Thakur, recently appointed as president, had undertaken to solve some of the management-employees problems by dealing directly with the individuals, as often as possible. The company did not have a history of strikes or any other form of collective action and was considered to have a good work culture. However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees. An important initiative of Mr. Thakur was to negotiate wages of the supervisors with each supervisor. In these negotiation meetings he would not involve anyone else, including the Personnel Department which reported to him, so as to take an unbiased decision. After negotiation, a wage contract would be drawn up for each supervisor. This, he felt, would recognise and reward the better performers. Mr. Thakur successfully implemented the process for most of the supervisors, except those working in the night shift. For them he had drawn up the contracts unilaterally benchmarking the wages of supervisors of night shift with that of supervisors of the day shift.
For several days Ram Lal a night shift supervisor, had been trying to seek an appointment with Mr. Thakur about his wages. He was disgruntled, not only over his failure to see the president, but also over the lack of discussions about his wage contract prior to its being effected. As a family man with six dependents, he felt his weekly wage should be higher than that granted to him.
Last Thursday afternoon Ram Lal stopped by the president’s office and tried to see him.
Mr. Thakur ’s secretary refused his request on the grounds that Mr. Thakur was busy.
Infuriated, Ram Lal stormed into the president’s office and confronted the startled Mr.
Thakur, with his demands for a better wage. Mr. Thakur stood up and told Ram Lal to get out of his office and express his grievance through official channel. Ram Lal took a swing at the president who in turn punched Ram Lal on the jaw and knocked him unconscious.

Q. The most important causal factor for this entire episode could be:

Detailed Solution for Test Level 3: Caselets - 2 - Question 17

The causal factor is clearly the inconsistent approach of Mr.Thakur where he is not consistent towards giving time to each of the supervisors in the company. It is this inconsistent approach of Mr. Thakur that has led to Ram Lal’s grievance and the subsequent escalation of the episode to an ugly one.
Option (d) is the correct answer.

Test Level 3: Caselets - 2 - Question 18

Directions: Re ad the following case let and choose the best alternative.

Mr. Rajiv Singhal, Chairman of the Board of Directors of Loha India Ltd., (a steel manufacturing company) had just been visited by several other directors of the company.
The directors were upset with recent actions of the company president, Mr. Ganesh Thakur. They demanded that the board consider firing the president.
Mr. Thakur, recently appointed as president, had undertaken to solve some of the management-employees problems by dealing directly with the individuals, as often as possible. The company did not have a history of strikes or any other form of collective action and was considered to have a good work culture. However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees. An important initiative of Mr. Thakur was to negotiate wages of the supervisors with each supervisor. In these negotiation meetings he would not involve anyone else, including the Personnel Department which reported to him, so as to take an unbiased decision. After negotiation, a wage contract would be drawn up for each supervisor. This, he felt, would recognise and reward the better performers. Mr. Thakur successfully implemented the process for most of the supervisors, except those working in the night shift. For them he had drawn up the contracts unilaterally benchmarking the wages of supervisors of night shift with that of supervisors of the day shift.
For several days Ram Lal a night shift supervisor, had been trying to seek an appointment with Mr. Thakur about his wages. He was disgruntled, not only over his failure to see the president, but also over the lack of discussions about his wage contract prior to its being effected. As a family man with six dependents, he felt his weekly wage should be higher than that granted to him.
Last Thursday afternoon Ram Lal stopped by the president’s office and tried to see him.
Mr. Thakur ’s secretary refused his request on the grounds that Mr. Thakur was busy.
Infuriated, Ram Lal stormed into the president’s office and confronted the startled Mr.
Thakur, with his demands for a better wage. Mr. Thakur stood up and told Ram Lal to get out of his office and express his grievance through official channel. Ram Lal took a swing at the president who in turn punched Ram Lal on the jaw and knocked him unconscious.

Q. Apart from the supervisors working the night shift, executives of which department will have the most justified reasons to be disgruntled with Mr.
Thakur’s initiative?
1. Production department—for not being consulted regarding the behaviour of the supervisors on the shop floor.
2. Finance department—for not being taken into confidence regarding the financial consequences of the wage contracts.
3. Marketing department—for not being consulted on the likely impact of the wage contracts on the image of the company.
4. Quality control—for not being able to give inputs to Mr. Thakur on how to improve quality of steel making process.
5. Personnel department—for it was their work to oversee wage policies for employees and they had been ignored by Mr. Thakur.

Detailed Solution for Test Level 3: Caselets - 2 - Question 18

From the given options, it is clear that there is a valid reason for the production department to feel aggrieved as Mr.Thakur has not consulted them regarding the behavior of the supervisors on the shop floor. Similarly, the Finance department is also affected as suggested in point number 2, while the Personnel department would definitely feel aggrieved and hence disgruntled as Mr. Thakur has ignored and even bypassed them in fixing wages of supervisors directly.
Hence, 1+2+5 represents the correct set of departments which have the most justified reasons for feeling disgruntled.
Hence, option (d) is the correct answer.

Test Level 3: Caselets - 2 - Question 19

Directions: Re ad the following case let and choose the best alternative.

Mr. Rajiv Singhal, Chairman of the Board of Directors of Loha India Ltd., (a steel manufacturing company) had just been visited by several other directors of the company.
The directors were upset with recent actions of the company president, Mr. Ganesh Thakur. They demanded that the board consider firing the president.
Mr. Thakur, recently appointed as president, had undertaken to solve some of the management-employees problems by dealing directly with the individuals, as often as possible. The company did not have a history of strikes or any other form of collective action and was considered to have a good work culture. However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees. An important initiative of Mr. Thakur was to negotiate wages of the supervisors with each supervisor. In these negotiation meetings he would not involve anyone else, including the Personnel Department which reported to him, so as to take an unbiased decision. After negotiation, a wage contract would be drawn up for each supervisor. This, he felt, would recognise and reward the better performers. Mr. Thakur successfully implemented the process for most of the supervisors, except those working in the night shift. For them he had drawn up the contracts unilaterally benchmarking the wages of supervisors of night shift with that of supervisors of the day shift.
For several days Ram Lal a night shift supervisor, had been trying to seek an appointment with Mr. Thakur about his wages. He was disgruntled, not only over his failure to see the president, but also over the lack of discussions about his wage contract prior to its being effected. As a family man with six dependents, he felt his weekly wage should be higher than that granted to him.
Last Thursday afternoon Ram Lal stopped by the president’s office and tried to see him.
Mr. Thakur ’s secretary refused his request on the grounds that Mr. Thakur was busy.
Infuriated, Ram Lal stormed into the president’s office and confronted the startled Mr.
Thakur, with his demands for a better wage. Mr. Thakur stood up and told Ram Lal to get out of his office and express his grievance through official channel. Ram Lal took a swing at the president who in turn punched Ram Lal on the jaw and knocked him unconscious.

Q. Out of the following, which one seems to be the most likely cause of Ram Lal’s grievance?

Detailed Solution for Test Level 3: Caselets - 2 - Question 19

Ram Lal’s grievance is brought about in the last two paragraphs of the passage.
A close reading of this should make you realise that Ram Lal’s principal grievance was due to the fact that since he was in the night shift, he did not get a chance to interact with the management regarding his wage fixation and his problems.
Option (b) is the correct answer.

Test Level 3: Caselets - 2 - Question 20

Directions: Re ad the following case let and choose the best alternative.

Mr. Rajiv Singhal, Chairman of the Board of Directors of Loha India Ltd., (a steel manufacturing company) had just been visited by several other directors of the company.
The directors were upset with recent actions of the company president, Mr. Ganesh Thakur. They demanded that the board consider firing the president.
Mr. Thakur, recently appointed as president, had undertaken to solve some of the management-employees problems by dealing directly with the individuals, as often as possible. The company did not have a history of strikes or any other form of collective action and was considered to have a good work culture. However, Mr. Thakur felt that by dealing directly with individuals, he could portray the management’s concern for the employees. An important initiative of Mr. Thakur was to negotiate wages of the supervisors with each supervisor. In these negotiation meetings he would not involve anyone else, including the Personnel Department which reported to him, so as to take an unbiased decision. After negotiation, a wage contract would be drawn up for each supervisor. This, he felt, would recognise and reward the better performers. Mr. Thakur successfully implemented the process for most of the supervisors, except those working in the night shift. For them he had drawn up the contracts unilaterally benchmarking the wages of supervisors of night shift with that of supervisors of the day shift.
For several days Ram Lal a night shift supervisor, had been trying to seek an appointment with Mr. Thakur about his wages. He was disgruntled, not only over his failure to see the president, but also over the lack of discussions about his wage contract prior to its being effected. As a family man with six dependents, he felt his weekly wage should be higher than that granted to him.
Last Thursday afternoon Ram Lal stopped by the president’s office and tried to see him.
Mr. Thakur ’s secretary refused his request on the grounds that Mr. Thakur was busy.
Infuriated, Ram Lal stormed into the president’s office and confronted the startled Mr.
Thakur, with his demands for a better wage. Mr. Thakur stood up and told Ram Lal to get out of his office and express his grievance through official channel. Ram Lal took a swing at the president who in turn punched Ram Lal on the jaw and knocked him unconscious.

Q. The situation with Mr. Lal could have been avoided if Mr. Thakur had 1. Delegated the task of negotiation of wage contracts for night shift employees to the Personnel department. 2. Created a process for supervisors working in the night shift so that they could have an opportunity to interact with him. 3. Created an open door policy that would have allowed employees to see him without any appointment. 4. Postponed the decision of wage revision for supervisors in the night shift for two months, since supervisors were rotated on different shifts after every two months.

The option that best arranges the above managerial interventions in decreasing order of organisational impact is:

Detailed Solution for Test Level 3: Caselets - 2 - Question 20

The best option is in the second intervention, i.e. creating a process for supervisors working in the night shift so that they could have an opportunity to interact with him. This would have solved the issue from the root and would in fact not allowed the issue to have cropped up at all.
The intervention in 3, is the next best one as it would have given Ram Lal an opportunity to meet Mr. Thakur without facing the red tapism of his secretary.
Consequently, Ram Lal’s grievances would have been heard and it would not have allowed the situation to escalate.
The only option which starts with interventions 2 and 3, is option (e).
Hence, option (e) is the correct answer.

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