# CAT Reasoning

Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee.

A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.

1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes - X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects.

An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.

Analyse the following caselet and answer the questions that follow:

Vimla is the domestic help for Shreya and her neighbour Padma; both live in a posh gated community. Vimla not only cleans the house, but also cooks for both the families. Shreya treasures Vimla ever since she joined her family four years ago. Vimla joined Padma’s household this year.

1. One evening Shreya trying to pay the pizza delivery was surprised to find a few five hundred rupee notes missing from her purse that she was sure were there earlier. She wants to ascertain if someone has stolen the money. On reflecting, the following facts crossed her mind:

1. In the last one year, Shreya had noticed cash missing on three occasions.
2. Shreya’s husband also shared that a few notes were missing from his wallet, though he was not sure if they were stolen.
3. Her eldest son had been pestering Shreya for more pocket money for the last three weeks; in the last few days, he had stopped doing so.
4. In the last one year, Vimla had received six mails from her family asking for money.
5. Her eldest son’s expenditure had gone up in the last few days.

Which of the following combinations of the above statements would DECREASE the likelihood that Vimla has stolen the money?

1. 1 and 3
2. 1 and 4
3. 1 and 5
4. 2 and 4
5. 3 and 5

2. Padma discovered some money missing from her purse. She suspects that Vimla has stolen it. She wants to prevent the stealing from happening again and is contemplating the following actions:

1. She should let it pass, since to err is human.
2. She should confront Vimla and tell her that she knows the truth and the act is unpardonable regardless of her past service and she is thinking of terminating her services.
3. She should tell Vimla that she is aware someone has stolen money from the house but is not sure who it is.
4. She should share with Vimla that neighbours think Vimla has stolen the money she doesn’t, but is interested in finding out the truth.
5. She should directly ask Vimla if she stole the money, promising her no punishment if she confesses.

Arrange the following combinations of the above actions in the DECREASING order of appropriateness.

1. 1, 5, 4
2. 2, 4, 1
3. 2, 5, 4
4. 3, 5, 4
5. 5, 2, 4

Analyse the following caselet and answer the question that follows:

Genius Consulting is a boutique consulting firm started by Shirish, Balram, Rahman and Xavier, four friends from a premier business school. They committed themselves to abide by two principles: a) not to indulge in anything unethical and b) share earnings equally.

Genius Consulting could not get a significant project till the following year, when they managed a big one after Rahman’s father referred their firm to his top management. Convinced of the team’s talent following an impressive presentation, the top management awarded them the project even though six other referred teams made presentations.

The day following the presentations, they met to decide the way forward for the organization. Which of the following choices would be the most appropriate for Genius Consulting?

1. As this project violates both their principles, Genius consulting should not take up the project.
2. Due to the violation of the first principle Genius consulting should not take up this project.
3. They should take up the project. Further, since Rahman had agreed to equal sharing, he is not entitled to finder’s fee.
4. They should take up the project and as the referral helped them survive, Rahman should be paid finder’s fee.
5. They should take up the project. But, in order not to violate the principles, Rahman can be paid finder’s fee this year and an equal amount be deducted from his compensation the next year.

Analyse the following caselet and answer the questions that follow:

Mrs Biswas was to retire in one year after serving in the construction department of the Gujarat government for more than thirty years. After retirement, she wanted to spend her retired life along with Mr Biswas, a retired school teacher in a small town in Kerala. They had two children, both studying in Bengaluru. The Biswas’ wished to construct a house in Kerala with their life savings.

The couple gathered information about owning a house in Kerala. They had four options:

1. Buy a fully furnished house from a big developer.
2. Buy a semi-furnished house from big developer and furnish it.
3. Get a local unregistered contractor to construct a house and furnish it.
4. Mr Biswas with inputs from the family could supervise the construction of a house back in Kerala by employing the best material, engineers, masons and labourers.

1. Which option would ENSURE the best control of quality of construction for the Biswas’?

1. The first option would ensure the best quality.
2. The second option would ensure the best quality.
3. The third option would ensure the best quality.
4. The fourth option would ensure the best quality.
5. Any of the options will equally ensure the best quality.

2. Which of the following additional information, IF TRUE, would improve the chances of the third option being preferred?

1. Based on the current information, with no additional information, the third is the best option.
2. Among local property holders, the contractor in the third option enjoys a good reputation.
3. Big developers are less open to changes in design.
4. Mr Biswas cannot stay back alone to supervise the construction.
5. The Biswas’ want to select the furniture on their own.

Analyse the following caselet and answer the questions that follow:

A pastor had eaten at restaurant with his troup of ten and his family. It is a norm to tip the waiter and about 20% of a waiter’s salary comes from these tips. However, while paying the bill, the pastor crossed out the automatic 18% tip charged for parties of more than eight and wrote “I give God 10% why do you get 18%?” above his signature. The chagrined waitress at the restaurant posted a photo of this on the social media. She was subsequently fired for violating company’s policy on customer privacy.

This would have been understandable if the restaurant had not posted just 2 weeks ago a customer receipt that was complimenting them. Social media and social activists came heavily upon the management’s ambivalent stand and the firing of the waitress. In response, the company posted a note on their social media page defending their actions. This quickly drew over 10,000 comments, mostly negative, to which the management started responding by posting the same note over and over again. There were also accusations of the company deleting negative comments and blocking users. The restaurant also experienced a sizable drop in their footfall.

1. Who/what is the main cause for the situation becoming unmanageable?

1. The pastor for flouting the norm of restaurant.
2. The waitress for violating customer privacy.
3. The management for not taking action against the pastor.
4. The management for giving out disproportionate punishment to waitress.
5. The management for removing negative comments from the social media.

2. The downward spiral continued for the restaurant as the management persisted in defending their actions and argued with those who criticised them. By the following week, the original post had generated over 18,000 negative comments. Which of the following is the best way forward for the restaurant at this juncture?

1. Unconditionally restore the waitress to her former position and salary on the ground that she was never at fault in the first place.
2. Apologise to and reinstate the waitress and ask her to apologize for her breach of customer privacy and post both the apologies on social media.
3. Reinstate the waitress provided she apologises for her breach of customer privacy and post that apology on the restaurant’s social media page.
4. Reinstate the waitress if and only if she apologizes for her breach of customer privacy and posts that apology on her social media page.
5. Recruit two waitress at a higher wage but stick to the original decision of firing the waitress.

Analyse the following caselet and answer the questions that follow:

A college campus with a population of around 2,000 of whom 200 were children, 1,200 people between 15 and 45 years, 500 people between 45 and 65 and around 100 people more than 65 years of age. The campus has two big gates opening out to the city. There are 400 cars and 500 motorbikes inside the campus. The residents relied on these vehicles to visit the city located 10 kilometres away.

Now, with land within the campus becoming scarce, the chief administrator (CA) found the growing demand for parking lot difficult to handle. The faculty, staff and students wanted increased parking space. In the past six years, the parking requirement on campus had doubled. The CA found it inappropriate to construct parking lots from the students’ fee, even though those with vehicles may not complain about it.

Besides creating parking problems, the CA felt that these vehicles added to the pollution and made residents less responsible toward each other. The risk to the children and the elderly because of over-speeding was menacing. Therefore, the CA wanted to reduce the number of vehicles in the campus. Many faculty members, students and staff members, however, felt that demand for more parking space was natural as vehicles were required to go to the market, railway station, airport, and inter-state bus terminal all located in the city. They also told the CA that the elderly, sick and the toddlers relied only on these vehicles. After listening to all stakeholders, the CA wanted to solve these problems while ensuring the campus remained responsible and green.

1. Which of the following actions would best satisfy all the stakeholders within the campus?

1. Levy extra fee on students to construct additional parking lots inside the campus. Students should pay for up-keep of the campus.
2. Let all vehicles be parked in a college-managed space outside the campus while two battery operated vehicles handle exigencies inside the campus.
3. Bring all stakeholders to the discussion table.
4. To reduce carbon footprints, only pooled vehicles should be allowed to operate inside the campus.
5. Charge significant fee from any vehicle entering or leaving the campus.

2. Which of the following would be the best option to increase revenue, decrease carbon footprint and still satisfy all the stakeholders in the campus?

1. Make substantial collection from vehicles entering or leaving campus and construct a parking lot outside the campus.
2. Levy extra fee on the students and build extra parking lots inside the campus.
3. Bring all stakeholders to table and let them build consensus.
4. To reduce the carbon footprint, only pooled vehicles be permitted on campus.
5. Let all vehicles be parked in a managed space outside the campus while battery operated vehicles parked at the two gates can be use inside the campus.

Analyse the following caselet and answer the questions that follow:

Girirajan an unemployed youngster from Kumbakonam, Tamilnadu, visited Singapore where his school friend worked as software engineer. In Singapore, Girirajan realized that there were a lot of Tamils in "Little India" area. He soon assessed that there were very few restaurants serving authentic Tamil food and decided to set-up a restaurant "Giri’s" in "Little India" serving authentic Tamil food in traditional banana leaf. Customers loved the food. Very soon word spread about the good quality food served in the traditional way. Girirajan expanded operation recruiting 10 employees, all Tamils.

Six months later, Girirajan realized that a lot of Kannadiga and Telugu customers started visiting the restaurant along with their Tamil friends. One day, a Kannadiga customer looking for Devangere Benne Dosa suggested that it may not be a bad idea for Girirajan to serve Karnataka and Andhra cuisines along with Tamil.

With time, the popularity of the restaurant kept soaring. As a result, a lot of Malays, Indonesians and Chinese started visiting the restaurant. His software engineer friend advised to cater to customers of all nationalities. Despite his desire to go grand, Girirajan realized he did not have enough money to get extra space anywhere in Singapore and banks were also reluctant to lend.

One day, while assessing the business, he realized that the restaurant had 90% occupancy rate during peak hours and 40% during the non-peak hours. Both figures were increasing with time.

1. Which of the following options would be most suitable for the growth of the business?

1. Include Karnataka and Andhra cuisines in the menu.
2. Include Indonesian and Chinese in the menu.
3. Keep the focus on Tamil food only with an increased focus on quality improvement.
4. Expand to include either Karnataka and Andhra cuisines or Indonesian and Chinese cuisines.
5. Include Karnataka and Andhra cuisines as well as Indonesian and Chinese.

Analyse the following caselete and answer the question that follows:

As a newly started organization in the IT sector, Saksha IT is a fast growing 400 employee organization. Its head, Saksha Kumar believes in building an organization driven by humility. Which of the following policies would best help him achieve that?

1. Employees shall, in their annual evaluation form, be asked to acknowledge three of their shortcomings, overcoming which will make them better.
2. Employees shall be asked to share with their peers three shortcomings they had noticed about their peers.
3. The immediate superiors would suggest three shortcomings their subordinates have to work on in a given period.
4. Everyone beginning with Saksha, shall be asked to share three of their weaknesses, in a public forum.
5. Employees shall be asked to overcome three shortcomings in the following year. Improvement, if noticed would attract rewards.

Analyse the following caselete and answer the question that follows:

Principal Maheshwari of BINK School of Management is facing a problem that calls for quick action. She received an anonymous mail one day, possibly from one of the students, complaining about outdated syllabi, medicore teachers and poor choice of courses on offer.

Which of the following is the best course of action available to the Principal?

1. She should invite students to discuss any problem openly, one on one or in small groups, promise to act on them but firmly condemn the culture of anonymous mails.
2. She should update the students about the efforts the institute is taking in sprucing up the syllabi, hiring talented faculty etc., but make no reference to the letter.
3. She should convene a meeting of the faculty at the earliest and get them to work on updating the syllabi and also arrange a faculty development program but keep mum about the letter.
4. She should convene a meeting of the faculty and talk about the letter as a symptom of a deeper malaise, ask them to update the syllabi and also organize a faculty development program.
5. She should ignore the letter and not think about it at all.

Answer the questions on the basis of the information given below.

Seven varsity basketball players (A, B, C, D, E, F, and G) are to be honoured at a special luncheon. The players will be seated on the dais in a row. A and G have to leave the luncheon early and so must be seated at the extreme right. B will receive the most valuable player's trophy and so must be in the centre to facilitate presentation. C and D are bitter rivals and therefore must be seated as far apart as possible.

1. Which of the following cannot be seated at either end?

1. F
2. G
3. C
4. D

2. Which of the following pairs cannot be seated together?

1. D & G
2. C & F
3. B & D
4. E & A

Answer the questions on the basis of the information given below.

Anju, Bimla, Charu and Dimple stay in the same colony and study in different schools. Their schools are in North, South, East and West direction w.r.t. the colony in no particular order. Anju’s school and Bimla’s school are located in opposite directions while Dimple’s school is located 90° clockwise w.r.t. Bimla’s school. The distance of the four schools from the colony is 100 units, 150 units, 200 units and 250 units in no particular order. Dimple’s school is located in West. Anju’s school is not the one closest to the colony while Charu’s school is closer to the colony than Dimple’s school. The school located in South is farthest from the colony.

1. If the school located in North is closer to the colony than the school located in West, then who studies in the school located at a distance of 150 units from the colony?

1. Bimla
2. Charu
3. Anju
4. Dimple

2. If Anju’s school is the one located at a distance of 200 units from the colony, then how far from the colony is the school located in West?

1. 100 units
2. 150 units
3. 200 units
4. 250 units

Answer the questions on the basis of the information given below.

A jeweller has 8 beads which he wants to use in making a necklace. There are 3 different beads of Red color - Striped Red, Matt Red and Sparkling Red. Similarly, there are 3 different beads of Blue color - Striped Blue, Matt Blue and Sparkling Blue. The other two beads are Green and Yellow in color respectively.

The conditions given below must be followed while making the necklace.

1. Striped Red and Striped Blue beads must always be put adjacent to each other.
2. Green and Yellow beads must always be put adjacent to each other.
3. No two beads of same color should be put adjacent to each other.

1. If none of the other two Red beads is to be put opposite the Striped Red bead then which of the following statements can be true?

2. If one of the other two Red beads is to be put opposite the Striped Red bead then which of the following statements can never be true?

1. The Yellow bead is put opposite the Striped Blue bead and the Sparkling Red bead is put opposite the Sparkling Blue bead.

Answer the questions on the basis of the information given below.

Four friends - Vikrant, Vikram, Jasneet and Saurabh - were born in four different months – January, March, July and December – of the same year, not necessarily in the same order. Each friend has a distinct surname among Joshi, Singh, Gupta and Agarwal, not necessarily in the same order. It is also known that:

1. Vikrant is younger than Gupta.
2. Jasneet was not born in December.
3. Saurabh, who is not the youngest, was not born in March.
4. Joshi is not the youngest and was also not born in January.
5. Vikram was born before Vikrant but after Agarwal.
6. Agarwal was not born in January.

1. Who among the four friends is the youngest?

1. Vikram Gupta
2. Vikrant Singh
3. Vikrant Joshi
4. Cannot be determined

2. Who among the four friends was born in March?

1. Jasneet Agarwal
2. Saurabh Gupta
3. Vikram Gupta
4. Cannot be determined

Answer the questions on the basis of the information given below.

Seven books, two each of Mathematics and Chemistry and three of Physics, are to be placed in order on a shelf. The two Mathematics books are of Algebra and Geometry, the two Chemistry books are of Organic and Inorganic and the three Physics books are of Kinetics, Thermodynamics and Electromagnetics.

The following conditions are to be kept in mind while placing the books:

1. All the books of a subject must be placed together.
2. The Chemistry books should be placed between Mathematics and Physics books.
3. The Thermodynamics book must be placed before the Electromagnetics book.
4. The Algebra book must be placed before the Geometry book.

1. If the Electromagnetics book is placed immediately before the Kinetics book, then which of the following statements may be true?

1. The Geometry book is placed at the seventh position.
2. The Thermodynamics book is placed at the second position.
3. The Thermodynamics book is placed at the third position.
4. The Geometry book is placed at the sixth position.

2. If a Chemistry book is placed adjacent to the Thermodynamics book, then which of the following statements must be false?

1. The Electromagnetics book is placed before the Kinetics book.
2. The Inorganic book is placed before the Thermodynamics book.
3. The Kinetics book is placed before the Geometry book.
4. The Kinetics book is placed before the Electromagnetics book.

Answer the questions on the basis of the information given below.

Four teams - Alveston, Blackpool, Chelsea and Dunstable - reached the semifinal stage in a football tournament. Two of the four teams played against each other in the first semifinal and the rest two played against each other in the second semifinal. The winners of these two matches played the final and the winner of the final match was declared the Champion of the tournament. The following observations were made during the semifinals and the final match:

1. Ten goals were scored in the three matches. At least one goal was scored by each of the four teams. Each team scored a distinct number of goals.
2. The team that scored the maximum number of goals in the three matches was not the Champion of the tournament.
3. Alveston did not play against Blackpool but Chelsea played against Dunstable.
4. Neither Blackpool nor Dunstable was the Champion of the tournament. The absolute difference between the total goals scored by these two teams in the three matches was 2.

1. How many goals were scored in the final match of the tournament?

1. 1
2. 2
3. 3
4. 4

2. How many goals did the Champion of the tournament score in its semifinal match?

1. 1
2. 2
3. 3
4. 4

Answer the questions on the basis of the information given below.

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are only two married couples in the group. The lawyer is married to D, who is a housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

1. Which of the following is one of the married couples?

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

2. What is E's profession?

1. Professor
2. Engineer
3. Lawyer
4. Accountant

3. How many members of the group are males?

1. 1
2. 2
3. 3
4. 4

Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare up to 3 portions of fries at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However fries cannot be prepared in anticipation of future orders.

A study to look at the early leaming of rural kids was carried out in a number of villages spanning three states, chosen from the North East (NE), the West (W) and the South (S). 50 four-year old kids each were sampled from each of the 150 villages from NE, 250 villages from W arid 200 villages from S. It was found that of the 30000 surveyed kids 55% studied in primary schools run by government (G), 37% in private schools (P) white the remaining 8% did not go to school (O).

Applicants for the doctoral programmes of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection.

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 a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:

6 1 2 4 3
9 5 3 2 8
7 8 4 6 5
3 9 5 1 2
1 7 6 3 9

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule.

The underlying principle that they are working on is the following:

Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.

Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute.

Funky Pizzaria was required to supply pizzas to three different parties. The total number of pizzas it had to deliver was 800, 70% of which were to be delivered to Party 3 and the rest equally divided between Party 1 and Party 2.

Pizzas could be of Thin Crust (T) or Deep Dish (D) variety and come in either Normal Cheese (NC) or Extra Cheese (EC) versions. Hence, there are four types of pizzas: T-NC, T-EC, D-NC and D-EC. Partial information about proportions of T and NC pizzas ordered by the three parties is given below:

There were seven elective courses - E1 to E7 - running in a specific term in a college. Each of the 300 students enrolled had chosen just one elective from among these seven. However, before the start of the term, E7 was withdrawn as the instructor concerned had left the college. The students who had opted for E7 were allowed to join any of the remaining electives. Also, the students who had chosen other electives were given one chance to change their choice. The table below captures the movement of the students from one elective to another during this process. Movement from one elective to the same elective simply means no movement. Some numbers in the table got accidentally erased; however, it is known that these were either 0 or 1.

An old woman had the following assets:

1. Rs. 70 lakh in bank deposits
2. 1 house worth Rs. 50 lakh
3. 3 flats, each worth Rs. 30 lakh
4. Certain number of gold coins, each worth Rs. 1 lakh

She wanted to distribute her assets among her three children; Neeta, Seeta and Geeta.

The house, any of the flats or any of the coins were not to be split. That is, the house went entirely to one child; a flat went to one child and similarly, a gold coin went to one child.

At a management school, the oldest 10 dorms, numbered 1 to 10, need to be repaired urgently, The following diagram represents the estimated repair costs (in Rs. Crores) for the 10 dorms. For any dorm, the estimated repair cost (in Rs. Crores) is an integer. Repairs with estimated cost Rs. 1 or 2 Crores are considered light repairs, repairs with estimated cost Rs. 3 or 4 are considered moderate repairs and repairs with estimated cost Rs. 5 or 6 Crores are considered extensive repairs.

A tea taster was assigned to rate teas from six different locations - Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal. These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information is given below:

In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.

The columns are labelled a to h (left to right) and the rows are numbered 1 to 8 (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position c5 means that the piece is in cth column and 5th row.

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.

The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.