List of top Decision Making Questions on Analytical Decision Making asked in XAT

Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.

There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.

Tech predictions often fail not because of wrong models or a lack of imagination, but due to lack of humility in admitting our uncertainty about the future.( Maximum 250 words )

Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. (Expected value is the sum of possible outcomes weighted by their probability of occurrence.) Preference for a sure outcome over a risky prospect of equal expected value is called risk averse; indeed, people tend to be risk averse when choosing between prospects with positive outcomes. The tendency towards risk aversion can be explained by the notion of diminishing sensitivity, first formalized by Daniel Bernoulli in 1738. Just as the impact of a candle is greater when it is brought into a dark room than into a room that is well lit, so, suggested Bernoulli, the utility resulting from a small increase in wealth will be inversely proportional to the amount of wealth already in one's possession. It has since been assumed that people have a subjective utility function, and that preferences should be described using expected utility instead of expected value. According to expected utility, the worth of a gamble offering a 50 percent chance to win $200 (otherwise nothing) is \(0.50 \times u(200)\), where \(u\) is the person's concave utility function. (A function is concave or convex if a line joining two points on the curve lies entirely below or above the curve, respectively.) It follows from a concave function that the subjective value attached to a gain of $100 is more than 50 percent of the value attached to a gain of $200, which gives a preference for the sure $100 gain and, hence, risk aversion.

Consider now a choice between losses. When asked to choose between a prospect that offers a 50 percent chance to lose $200 (otherwise nothing) and the alternative of losing $100 for sure, most people prefer to take an even chance at losing $200 or nothing over a sure $100 loss. This is because diminishing sensitivity applies to negative as well as to positive outcomes: the impact of an initial $100 loss is greater than that of the next $100. This gives a convex function for losses and a preference for risky prospects over sure outcomes of equal expected value, called risk seeking. Except for prospects that involve very small probabilities, risk aversion is generally seen in choices involving gains, while risk seeking tends to hold in choices involving losses.

Based on the above passage, look at the decision situations faced by three persons: Babu, Babitha and Bablu.

Suppose the instant and further utility of each unit of gain is the same for Babu. Babu has decided to play as many times as possible before he dies. He expects to live for another 50 years. A game does not last more than ten seconds. Babu is confused about which theory to trust for making his decision and seeks the help of a renowned decision making consultant, Roy Associates. What should Roy Associates' advice to Babu be?

Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Presented with a choice between a risky prospect that offers a 50 percent chance to win $200 (otherwise nothing) and an alternative of receiving $100 for sure, most people prefer the sure gain over the gamble, although the two prospects have the same expected value. Preference for a sure outcome over a risky prospect of equal expected value is called risk averse; people tend to be risk averse when choosing between prospects with positive outcomes, a pattern explained by diminishing sensitivity: the utility from a small increase in wealth falls as the wealth already held rises, so the person's utility function \(u\) is concave for gains. A convex utility function is the mirror image of this: it gives MORE weight to the extreme, spread-out outcome of a gamble than to a 'safer,' more sure-like outcome of the same expected value, and a person with such a function is called risk taking or risk seeking.

Based on the above, look at the decision situation faced by Babitha.

Babitha played a game in which she had three options, with probabilities 0.4, 0.5 and 0.8 respectively. The gains from the three outcomes are likely to be $100, $80 and $50 respectively. An expert has pointed out that Babitha is a risk taking person. According to the expected utility hypothesis, which option is Babitha most likely to favour?

Recall Babitha's game: three options with probabilities 0.4, 0.5 and 0.8, giving likely gains of $100, $80 and $50 respectively (all three have the same expected value of $40, and Babitha, being risk taking, was shown to favour the first, most spread-out option when she can play repeatedly).

Continuing with the previous question, suppose Babitha can only play one more game. Which theory would help in arriving at a better decision?

Decisions are often 'risky' in the sense that their outcomes are not known with certainty. Expected value is the sum of possible outcomes weighted by their probability of occurrence, and a preference between prospects can be judged purely on this basis under the expected value hypothesis, without reference to any personal utility function. Utility functions, and the concepts of concave (risk averse) or convex (risk seeking) curvature, belong to the SEPARATE expected utility hypothesis, not to expected value itself, which is just a plain, objective weighted sum.

Based on the above, look at the decision situation faced by Bablu.

Bablu had four options with probabilities of 0.1, 0.25, 0.5 and 1 respectively. The gains associated with each option are $1000, $400, $200 and $100 respectively. Bablu chose the first option. As per the expected value hypothesis:

Read the following situation and choose the best possible alternative.

A database software company found out that a product it had recently launched had a few bugs. The product had already been bought by more than a million customers. The company knew that these bugs could cost its customers a lot of money or trouble. However, if it told customers about the bugs, it was afraid of losing its credibility in the market. What would be the most ethical option for the company?

Read the following situation and choose the best possible alternative.

The city of Nagar has a population of 10 million: 2 million are rich, 3 million are poor and 5 million belong to the middle class. Saundarya Cosmetics makes and sells beauty products to the rich class at a premium price, and its products are very popular with these customers. Many people from the middle and poor segments want to buy these products but cannot afford them because of the high prices. Lately, sales growth in the rich segment has been slowing down. Which of the following is the best option for Saundarya Cosmetics to increase its profits over the long term?

Read the following situation and choose the best possible alternative.

Seema was a finance manager at an MNC and felt that gender discrimination at her workplace was slowing down her career. Frustrated, she quit her job and started her own company. When she started the company, Seema decided to keep an equal number of male and female employees. Over the last six years, Seema has become a very successful entrepreneur and has grown her business to eight locations across the country. Recently, however, Seema has run into an ethical problem: many of her female employees are not willing to travel between cities or work late hours, even though the job needs this, while her male employees do this without hesitation. Seema is now under pressure to reduce the number of female employees, but she also knows that hiring equal numbers of men and women was one of the strongest reasons she started the company in the first place. What should she do as a responsible woman entrepreneur?

Read the following situation and choose the best possible alternative.

You are a recruitment manager interviewing Mayank, a hard-working young man who has trouble speaking fluent English because he studied in schools and colleges that used a regional language as the medium of instruction. If your company currently has open positions, what would you choose to do?

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

Which of the following statements must be true?

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

If the Professor conducts a quiz on Tuesday, then her schedule for evaluating quizzes could be:

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

Which one of the following must be a day on which the professor lectures?

Directions: Professor Mukhopadhay works only on Mondays, Tuesdays, Wednesdays, Fridays, and Saturdays. She performs four different activities: lecturing, conducting quizzes, evaluating quizzes, and working on consultancy projects. Each working day she performs exactly one activity in the morning and exactly one activity in the afternoon. Her weekly schedule must satisfy all of the following restrictions:

1. She conducts quizzes on exactly three mornings.
2. If she conducts a quiz on Monday, she does not conduct a quiz on Tuesday.
3. She lectures in the afternoon on exactly two consecutive calendar days.
4. She evaluates quizzes on exactly one morning and three afternoons.
5. She works on a consultancy project on exactly one morning.
6. On Saturday, she neither lectures nor conducts a quiz.

On Wednesdays, the professor could be scheduled to:

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Q125. The second best option (in terms of travel time) gives a total travel time of ______ hours for the entire itinerary.

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Q126. Due to winter fog, flights out of Delhi have become uncertain and unreliable. Given this constraint, the itinerary Ram should adopt to have the best probability of reaching Ajmer on time is:

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Q127. Ram's younger brother Shyam gets to know of Ram's travel plans and wants to come along. Unlike Ram, Shyam enjoys the scenery en route and wants Ram to maximise the total travel time. To do this, the itinerary Ram should decide on is:

I. Delhi to Bharatpur by train; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by bus; Jaipur to Ajmer by bus
II. Delhi to Bharatpur by bus; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by taxi; Jaipur to Ajmer by taxi
III. Delhi to Bharatpur by bus; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by bus; Jaipur to Ajmer by bus
IV. Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by taxi; Jaipur to Ajmer by bus
V. Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by taxi; Jaipur to Ajmer by taxi

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Ram's statistically minded friend Rocky feels that Ram should not use just one criterion to decide on a plan. "Decision making has to bring in all the criteria together. That is what makes a decision sound," Rocky said.

"How do I do that?" Ram asked. "Simple," said Rocky. "Give a weight to each criterion, multiply the value of each criterion by its weight, and add up the products for each option."

Rocky explained with an example: "For each option there are two criteria, the probability of not making it to the wedding and the travel time. The probability of not reaching on time is 1 minus the probability of reaching on time. Say you hate the thought of missing the wedding after all this effort, so give that criterion a weight of 80%. You also want to keep the travel time low, so give that a weight of 20%. For each option, add up (value of each criterion times its weight) and compare the totals across options. Pick the option with the lowest total."

"That simple?" Ram asked. "Well, it is, for a start," Rocky admitted.

Q128. As the foggy winter conditions continue, flights out of Delhi remain uncertain and unreliable. Using Rocky's elementary decision-making framework, which of the following itineraries should Ram adopt?

Directions for Q125-129: The following set of questions is based on a decision-making situation described below. Read the passage and answer the questions that follow.

Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend's marriage in Ajmer, Rajasthan. He has barely managed to get leave from his boss, so he must make sure he reaches Ajmer at least on the day of the marriage. Since it had been a while since his last break, he also planned to visit a few tourist spots along the way to de-stress after a year of demanding work.

As per his plan, Ram would start from Delhi and first visit the Bharatpur bird sanctuary, staying at the forest guest house for some time. He would then travel to Jodhpur for a day or two of sightseeing, and from Jodhpur move to Jaipur to spend a few days visiting the city. After that he would travel on to Ajmer, where his friend's wedding would take place.

Leg 1, Delhi to Bharatpur (bus, taxi or train, all three taking 12 hours): the probability of reaching on time is 0.65 by bus, 0.75 by taxi and 0.9 by train.
Leg 2, Bharatpur to Jodhpur (train, bus or private taxi): the probability of reaching on time is 0.9 by train (12 hours), 0.8 by bus (16 hours) and 0.85 by taxi (14 hours).
Leg 3, Jodhpur to Jaipur (flight, train, bus or taxi): the probability of reaching on time is 0.85 by flight (2 hours), 0.9 by train (10 hours), 0.65 by bus (15 hours) and 0.7 by taxi (15 hours).
Leg 4, Jaipur to Ajmer (train, bus or taxi): the probability of reaching on time is 0.75 by train (4 hours), 0.55 by bus (5 hours) and 0.55 by taxi (5 hours).

Since both Jaipur and Jodhpur have airports, Ram could also fly directly from Delhi to either city, or use a flight partway along with a combination of land transport.

Ram's statistically minded friend Rocky feels that Ram should not use just one criterion to decide on a plan. "Decision making has to bring in all the criteria together. That is what makes a decision sound," Rocky said.

"How do I do that?" Ram asked. "Simple," said Rocky. "Give a weight to each criterion, multiply the value of each criterion by its weight, and add up the products for each option."

Rocky explained with an example: "For each option there are two criteria, the probability of not making it to the wedding and the travel time. The probability of not reaching on time is 1 minus the probability of reaching on time. Say you hate the thought of missing the wedding after all this effort, so give that criterion a weight of 80%. You also want to keep the travel time low, so give that a weight of 20%. For each option, add up (value of each criterion times its weight) and compare the totals across options. Pick the option with the lowest total."

"That simple?" Ram asked. "Well, it is, for a start," Rocky admitted.

For reference, the five itineraries under discussion (labelled A to E on the x-axis of each bar chart) are:
A: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by bus; Jaipur to Ajmer by train
B: Delhi to Bharatpur by taxi; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train
C: Delhi to Bharatpur by train; Bharatpur to Jodhpur by train; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
D: Delhi to Bharatpur by train; Bharatpur to Jodhpur by taxi; Jodhpur to Jaipur by train; Jaipur to Ajmer by train
E: Delhi to Bharatpur by train; Bharatpur to Jodhpur by bus; Jodhpur to Jaipur by flight; Jaipur to Ajmer by train

Q129. Of the diagrams given as options, which one best represents the contribution of each of the two criteria to the overall score, for each of the five itineraries A to E listed above, where the bottom portion of each bar shows the contribution of the probability of NOT reaching the destination on time, and the top portion shows the contribution of travel time?

Directions: Each group of questions in this section is based on a set of conditions. Choose the response that most accurately and completely answers each question.

(Questions 108 to 112): Krishnapuram's town council has exactly three members: Arjun, Karn, and Bhim. During one week, the council members vote on exactly three bills: a recreation bill, a school bill, and a tax bill. Each council member votes either for or against each bill. The following is known:

• Each member of the council votes for at least one of the bills and against at least one of the bills.
• Exactly two members of the council vote for the recreation bill.
• Exactly one member of the council votes for the school bill.
• Exactly one member of the council votes for the tax bill.
• Arjun votes for the recreation bill and against the school bill.
• Karn votes against the recreation bill.
• Bhim votes against the tax bill.

112. If one of the members of the council votes against exactly the same bills as does another member of the council, then which one of the following statements must be true?

(Questions 115 to 117): The year 2004 was a great year for Top-Cloth cotton mill. Manufacturing towels for the export market and employing more than 2000 workers, the company had an impressive growth in sales and profits. The Chairman felt that employees were entitled to a share in the profits, and it was proposed that the employee mess be air-conditioned. The proposal was discussed in a meeting attended by, among other senior officials, the marketing director, the personnel director and the finance director. The proposal was based on the fact that the shop floor of the mill often had temperatures in excess of 40 degrees C with a relative humidity of 99%. The air-conditioned mess would represent management's appreciation of the employees' hard work.

At the end of 2005, management reviewed the mill's performance. Profits were higher, and employee attrition was negligible. The Chairman decided that employees deserved additional recognition for their fine work. Since the mess had already been air-conditioned, the Chairman wanted to know if the employees appreciated this sort of action. In the course of discussion, the Chairman asked the personnel director to send a questionnaire to a sample of fifty employees and obtain their reaction to the air-conditioned mess. The management agreed to decide only after obtaining the feedback from the employees.

The personnel director mailed a simple form to fifty employees, asking them for the following information: "Please state your reaction to the air-conditioned mess." Of the fifty forms mailed, forty-six were returned. The answers received were as follows:

Reaction	Frequency
"I did not know it was air-conditioned."	16
"I never eat there"	8
"If management can spend money like that, they should pay us more"	6
"I wish the entire mill was air-conditioned."	8
"The mess is for management employees."	4
"It is OK."	2
Miscellaneous comments	2

116. Management of Top-Cloth cotton mill considers itself to be socially conscious, and its decisions are often re-examined for their social relevance and their impact on society. In view of this consideration, what could have been considered before deciding on profit sharing?
A. communicating management's intentions via employee newsletters
B. taking employees' inputs in designing the cafeteria's interiors and installation of air-conditioning
C. considering employees' views on different ways of sharing excess profits
D. investing in capacity expansion to take care of the booming export market
E. dividing the profits equally among the workers and shareholders
The options in decreasing order of their impact on society:

Directions: Each group of questions is based on a set of conditions. Read the passage below and answer the question that follows.

A retail electronics chain has six new mobile phone models, T, V, W, X, Y and Z. Each model comes with at least one of three options: digital camera, music player and office document viewer. No model has any other option. The following conditions apply:

• V has both a digital camera and an office document viewer.
• W has a digital camera and a music player.
• W and Y have no options in common.
• V and Z have exactly one option in common.
• T has fewer options than Z.

For this question only, replace the rule "X has more options than W" with this new rule: "X and W have exactly two options in common." All the other rules above still apply.

Which one of the following must be false?

Directions: Each group of questions is based on a set of conditions. Read the passage below and answer the question that follows.

Krishnapuram's town council has exactly three members: Arjun, Karn and Bhim. During one week the council votes on exactly three bills: a recreation bill, a school bill and a tax bill. Each member votes either for or against each bill. The following is known:

• Each member votes for at least one of the bills and against at least one of the bills.
• Exactly two members vote for the recreation bill.
• Exactly one member votes for the school bill.
• Exactly one member votes for the tax bill.
• Arjun votes for the recreation bill and against the school bill.
• Karn votes against the recreation bill.
• Bhim votes against the tax bill.

Which one of the following statements could be true?

Directions: Each group of questions is based on a set of conditions. Read the passage below and answer the question that follows.

Krishnapuram's town council has exactly three members: Arjun, Karn and Bhim. During one week the council votes on exactly three bills: a recreation bill, a school bill and a tax bill. Each member votes either for or against each bill. The following is known:

• Each member votes for at least one of the bills and against at least one of the bills.
• Exactly two members vote for the recreation bill.
• Exactly one member votes for the school bill.
• Exactly one member votes for the tax bill.
• Arjun votes for the recreation bill and against the school bill.
• Karn votes against the recreation bill.
• Bhim votes against the tax bill.

If the set of members of the council who vote against the school bill are the only ones who also vote against the tax bill, then which one of the following statements must be true?