The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.
Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.
77. The class on Wednesday started at:
The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.
Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.
77. The class on Wednesday started at:
Show Hint
- 7:05 am and the topic was ratio and proportion.
- 7:20 am and the topic was calculus.
- 7:00 am and the topic was calculus.
- 7:20 am and the topic was calculus.
The Correct Option is B
Solution and Explanation
Mr. Chatterjee is on Wednesday (given directly), so he is fixed there. Mr. Singh is not on Thursday and not on Monday (the clue says Mr. Singh did not teach the Monday class), so Mr. Singh must be on Wednesday or Friday. Since Wednesday already belongs to Mr. Chatterjee, Mr. Singh teaches on Friday.
Step 2: Use the Friday clue to fix Mr. Singh's topic.
The teacher in Friday's class taught set theory. Since Mr. Singh is on Friday, Mr. Singh taught set theory. This also fits the clue that Mr. Banerjee did not teach set theory, because Mr. Banerjee is a different person from Mr. Singh.
Step 3: Work out who taught probability.
Mr. Chatterjee (Wednesday) did not teach probability, and Mr. Singh (Friday) taught set theory, not probability. Mr. Banerjee cannot be the probability teacher either, because his class started five minutes after the class in which probability was taught, which means Mr. Banerjee and the probability teacher are two different people. That leaves only Mr. Dutta to teach probability, which fits the separate clue that Mr. Dutta did not teach ratio and proportion.
Step 4: Place Mr. Dutta and Mr. Banerjee on the remaining two days.
Monday and Thursday are left for Mr. Dutta and Mr. Banerjee. The Monday class started at 7:00 am. If Mr. Banerjee were on Monday, his start time would be 7:00 am, and the probability class, which starts five minutes before his class, would have to start at 6:55 am, before the earliest allowed time of 7:00 am. That is impossible, so Mr. Dutta is on Monday, teaching probability at 7:00 am, and Mr. Banerjee is on Thursday, at 7:00 am + 5 minutes = 7:05 am.
Step 5: Work out the topics left for Mr. Chatterjee and Mr. Banerjee.
Only ratio and proportion and calculus remain, for Mr. Chatterjee (Wednesday) and Mr. Banerjee (Thursday). Calculus was taught in the class that started at 7:20 am. Mr. Banerjee's class started at 7:05 am, so he did not teach calculus; he taught ratio and proportion. That leaves calculus for Mr. Chatterjee, so his Wednesday class started at 7:20 am, which also fits the clue that Wednesday's class did not start at 7:10 am.
Final Answer:
The full schedule is: Monday 7:00 am, Mr. Dutta, probability; Wednesday 7:20 am, Mr. Chatterjee, calculus; Thursday 7:05 am, Mr. Banerjee, ratio and proportion; Friday, Mr. Singh, set theory. So the class on Wednesday started at 7:20 am with calculus as the topic. In the original five-option paper this exact statement, 7:20 am and calculus, was printed twice, once as option B and once as option D, which made the question impossible to grade with a single unique correct choice. That duplication is why XAT officially dropped this question; on merit, the content shared by options B and D is the one that fits every clue. \[ \boxed{\text{7:20 am, calculus}} \]
Top XAT Decision Making Questions
- Direction: Read the following scenario and answer the questions that follow.
Riya, a brilliant young scientist, comes from a small town with limited resources and opportunities. Despite the challenges, Riya has always been passionate about scientific research and dreams of making groundbreaking discoveries. She excels in her studies and actively participates in science competitions, where she consistently wins accolades for her innovative projects. Riya's parents, although supportive, struggle to provide the financial means necessary to support her scientific pursuits. Determined to overcome these obstacles, Riya is ready to take the next steps towards achieving her dream.
To increase Riya's chances of realising her dream, which of the following actions should she prioritise? - Direction: Read the following scenario and answer the questions that follow.
Riya, a brilliant young scientist, comes from a small town with limited resources and opportunities. Despite the challenges, Riya has always been passionate about scientific research and dreams of making groundbreaking discoveries. She excels in her studies and actively participates in science competitions, where she consistently wins accolades for her innovative projects. Riya's parents, although supportive, struggle to provide the financial means necessary to support her scientific pursuits. Determined to overcome these obstacles, Riya is ready to take the next steps towards achieving her dream.
Riya successfully conducts several groundbreaking experiments and gains recognition for her contributions to the scientific community. She now wants to expand her research and collaborate with other scientists from around the world. Which strategy would be most effective for Riya to achieve this? - Direction: Read the following scenario and answer the questions that follow.
Riya, a brilliant young scientist, comes from a small town with limited resources and opportunities. Despite the challenges, Riya has always been passionate about scientific research and dreams of making groundbreaking discoveries. She excels in her studies and actively participates in science competitions, where she consistently wins accolades for her innovative projects. Riya's parents, although supportive, struggle to provide the financial means necessary to support her scientific pursuits. Determined to overcome these obstacles, Riya is ready to take the next steps towards achieving her dream.
With her ingenuity and determination, Riya finds a way to attract international collaborators and establish herself as a respected scientist in her field. However, she realises that her research findings are not effectively reaching the general public. To increase awareness and foster public interest in scientific research, which of the following options would be most beneficial for Riya? - Direction: Read the following scenario and answer the questions that follow.
Rahul is the CEO of a multinational corporation that operates in a country where discrimination based on caste is prevalent. Rahul has been urged by stakeholders to address the underrepresentation of individuals from marginalised castes in the company's workforce. However, Rahul is hesitant and unsure about the benefits and feasibility of actively promoting diversity in this regard.
The following arguments are presented to Rahul about the benefits of hiring individuals from lower castes:
1) Individuals from marginalised castes bring diverse perspectives, experiences, and cultural insights, which can foster innovation and creativity within the organisation.
2) Hiring individuals from marginalised castes can help reduce societal inequalities by providing them with opportunities for economic mobility and social upward mobility.
3) Creating an inclusive work environment that promotes diversity can attract top talent from all backgrounds, leading to a more competitive and successful organisation.
4) Individuals from marginalised castes often possess resilience, determination, and a strong work ethic due to the challenges they have faced, making them valuable assets to the company.
5) Promoting diversity and social inclusion can improve the company's reputation, enhance brand image, and attract a wider customer base.
From the above arguments, which of the following options indicate that Rahul's apprehensions are misplaced? - Direction: Read the following scenario and answer the questions that follow.
Rahul is the CEO of a multinational corporation that operates in a country where discrimination based on caste is prevalent. Rahul has been urged by stakeholders to address the underrepresentation of individuals from marginalised castes in the company's workforce. However, Rahul is hesitant and unsure about the benefits and feasibility of actively promoting diversity in this regard.
After careful consideration, Rahul decides to implement diversity initiatives to address the underrepresentation of individuals from marginalised castes in the company. Which of the following actions would be most effective in promoting diversity and inclusivity?
Top XAT Complex Arrangement Questions
In the country of Gagan, air travellers can buy their tickets either directly from the airlines or from three websites that are licensed to offer ticketing services online. In Gagan, most of the commercial transactions are done electronically, and all citizens have an account with its national bank, CeeCee. As a result, the three websites have become popular, and each transaction through these websites carries a surcharge of Gs. 250 (Gs. refers to Guppes, the currency of Gagan). Given below are four post new - year (January 2, 2011, to February 28, 2011) offers from three competing websites:
Cozy _ travel Offer: Make a con rmed booking for any service ( ight ticket, hotel or rail tickets) through Cozy_travel.com from December 5, 2010 to February 8, 2011 and become eligible for two free air tickets (offer is limited to the base fare). Free tickets have to be booked through online request from January 1, 2011 to February 28, 2011. The request for free tickets should be submitted at least twenty-one days in advance. Free tickets are non-amendable (except the passenger's name) and cannot be cancelled. Free ticket cannot be exchanged for cash or kind with anybody. Cozy_travel will try its best to secure the free ticket as per the request. However, ticket con rmation is subject to airline schedule and set availability in airlines selected and nalized by Cozy_travel from speci c available airlines.
Cool_yatra Offer: Book any air ticket of any airline on Cool_yatra.com on or after December 21, 2010 and get your next ticket free. Under this offer, only the base fare of the free ticket will be refunded by Cool_Yatra.com. The customer will have to bear the rest of the charges (other fees and surcharges). The value of the base fare will be refunded to the passenger on/after March 1 or fteen days after completion of travel on the free ticket (whichever is later). The free ticket can be booked only on Gaga Air ights. The free ticket must be booked within fteen days of booking the original ticket, and the travel date of the free ticket must be fteen days after the booking date of the free ticket. There must be a seven-day gap between the travel date of the main/original ticket and the free ticket. The travel date of the free ticket should be on or before February 28, 2011. The free ticket cannot be transferred. On cancellation of the original ticket(s), you no longer remain eligible for the free ticket(s).
Easy_travel Cash Back Offer: Easy travel offers 25% cash back on all air ticket bookings between December 5, 2010 and February 28, 2011 using CeeCee net banking service or its debit/credit card. The cashback amount will be credited back to the customer's account within twenty-one days of making the transaction. Maximum cashback during the period is Gs. 400 per person per ticket, and the total amount that can be claimed by the customer is Gs. 2,400.
Ek Ke Sath Ek Offer from Easy_travel: Book an AirSpice ticket with Easy_travel using any credit/debit card, and get another ticket absolutely free. The free tickets will be issued on AirSpice on its entire network. The offer is valid for sale from January 11, 2011 to January 31, 2011. The free ticket must be booked at least fteen days prior to the date of travel and needs to be completed within the offer period. The promotion code for the free ticket will get activated only seven days after booking the main ticket. Easy_travel will charge a handling fee of Gs. 1000/- per person for any amendments made on the main ticket. Cancellations of tickets purchased under this offer are not permitted. The free ticket obtained under this offer can not be exchanged for cash and cannot be re-routedGirirajan 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 reastaurant 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 gures were increasing with time.Geetha Gawde can cultivate up to 6 crops a year. Crop A and B are ready for harvest in 2 months; crop C and D in 3 months, and crop E and F in 4 months. Crop A can be cultivated from January to June; crop B can be cultivated from April to September; crop C can be cultivated from May to December; crops D as well as E can be cultivated from August to December, and crop F from November to May. If Geetha plans a change of crop the soil should be left fallow for one month; however, if the same crop is sown no fallow time is needed. Sowing takes place only at the beginning of a month. Geetha can only harvest a maximum of 1000 units of any crop at any point in time. The production cost per unit (incurred at the time of sowing) and price per unit of crop are as follows:
Crop Production Data
Crop Production cost per unit crop (in USD) Price per unit crop (in USD) A \(20\) \(60\) B \(5\) \(55\) C \(25\) \(70\) D \(15\) \(75\) E \(5\) \(65\) F \(35\) \(75\) 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 six 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 to Delhi.
A quick search revealed that ticket from Jamshedpur to Delhi is available in two 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 three-hour road trip and take a flight to Delhi from Ranchi. The distance between Ranchi and Delhi is covered in 105 minutes both-ways by any of the scheduled flights. Air India operates two flights, AI 9810 and AI 810, which depart Ranchi at 08:00 hrs 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 AI 809, 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 five 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 one hour before the scheduled departure to complete the boarding procedure. At every railway station she loses five minutes in navigating through the crowd.Dev Anand, CEO of a construction company, recently escaped a potentially fatal accident. Dev had failed to notice a red light while driving his car and attending to his phone calls. His well-wishers advised him to get a suitable replacement for the previous driver Ram Singh, who had resigned three months back. Ram Singh was not just a driver, but also a trusted lieutenant for Dev Anand for the last five years. Ram used to interact with other drivers, and gathered critical information that helped Dev in successfully bidding for different contracts. His inputs also helped Dev to identify some dishonest employees, and to retain crucial employees who were considering attractive offers from his competitors. Some of the senior employees did not like the informal influence of Ram and made it difficult for him to continue in the firm. Dev provided him an alternative job with one of his relatives.
During the last three months Dev has considered different candidates for the post. The back grounds of the candidates are given in the table below.Name Age Educational Qualification Experience Expected Salary / Remark Sunder 32 Post Graduate Seven years of driving experience 18,000 per month. Ex-employers are highly satisfied. Concern: tendency to switch jobs after every six months. Enjoys new jobs but loses interest after six months. Not willing to commit for more than six months. Mani 23 Studied up to Standard IX One year 8,000 per month. Claims to have more than one year of experience but can’t provide proof. Received a hike of 2,000 last month due to good performance. Chintan 44 Graduate 20 years 20,000 per month. Worked as driver for one year after losing stenographer job. Recommended to take up driver job. Bal Singh 40 Literate More than 20 years 15,000 per month. Cousin of Ram Singh. Substituted Ram as Dev’s driver when Ram was on leave. Currently working as driver with Dev’s in-laws. Strongly recommended by Ram. His knowledge and contacts in the firm are as good as Ram’s. Chethan 38 Standard XII 10 years 12,000 per month. Worked as temporary driver with Dev’s competitor for the last three years. Competitor recommended him to Dev. Expressed willingness for long-term job if given annual increment of 500. Dev is primarily looking for a stable and trustworthy driver, who can be a suitable replacement for Ram. His family members do not want Dev to appoint a young driver, as most of them are inexperienced. Dev’s driver is an employee of the firm and hence the appointment has to be routed through the HR manager of the firm. The HR manager prefers to maintain parity among all employees of the firm. He also needs to ensure that the selection of a new driver does not lead to discontent among the senior employees of the firm.
Top XAT Questions
- Ashok, a maths teacher in the school, asked his students to guess his date of birth by giving the following hints.
Hint 1: He was born in 1995
Hint 2: The sum of the products of his birth date multiplied by 24 and his birthday month multiplied by 60 is 1284.
Find the sum of Ashok’s birth date, birth month, and birth year. - Solve for the number of integral values of \(x: \frac{(x^2-15x+47)(x-13)}{(x-8)}<0\).
- In an examination, Akhil scored 11.11% less than the pass marks and Akshay scored 12.5% more than the pass marks. Find the percentage of pass marks if the sum of the scores of Akhil and Akshay is 25% more than the total marks.
- The ratio of paint and oil in Tank A is 3: 4, whereas in Tank B, the respective ratio is 4: 5 . Then, 96 liters of a mixture consisting of paint and oil in the ratio of 5: 1 is added to Tank A, such that the respective ratio in Tank A becomes exactly the reverse of that in Tank B. Find the amount (in liters) of the mixture from Tank B that is poured into Tank A such that the amount of paint and water in Tank A become equal.
- The points (–4, 3) and (–1, –4) are two end points of a diagonal of a parallelogram. If the other diagonal has the equation 7y + 3x + c = 0, then find the value of c.