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Previous Year Questions
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For any natural numbers m,n, and k, such that k divides both m+2n and 3m+4n,k must be a common divisor of
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In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
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A rectangle with the largest possible area is drawn inside a semicircle of radius 2cm . Then, the ratio of the lengths of the largest to the smallest side of this rectangle is
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Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is
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A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
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A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is
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There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is
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A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is
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The population of a town in 2020 was 100000. The population decreased by y% from the year 2020 to 2021, and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between x and y is 10, then the lowest possible population of the town in 2021 was
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Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be
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Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be
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The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
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How many times does Team 4 pass through Station E in a day?
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How many teams pass through Station C in a day?
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A, B, C, D, E and F are the six police stations in an area, which are connected by streets as shown below. Four teams – Team 1, Team 2, Team 3 and Team 4 –
patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.
The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time.
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs.
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs.
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs.
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E.
6. Team 4 never passes through Stations B, D or F.
Which one among the following stations is visited the largest number of times?
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How many times do the teams pass through Station B in a day?
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Which team patrols the street connecting Stations D and E at 10:15 hrs?
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How many times does Team 4 pass through Station E in a day?
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How many teams pass through Station C in a day?
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Which one among the following stations is visited the largest number of times?
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How many times do the teams pass through Station B in a day?
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Which team patrols the street connecting Stations D and E at 10:15 hrs?
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An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.
The following information is also known: 1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs. 3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.
How many Split Inverter ACs did D2 sell?
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What percentage of ACs sold were of Non-inverter type?
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What was the total number of ACs sold by D2 and D4?
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Which of the following statements is necessarily false?
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If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
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How many Split Inverter ACs did D2 sell?
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What percentage of ACs sold were of Non-inverter type?
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What was the total number of ACs sold by D2 and D4?
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Which of the following statements is necessarily false?
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If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
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What was the number of online registrations in January?
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Which of the following statements can be true?
I. The number of offline registrations was the smallest in May.
II. The total number of registrations was the smallest in February.
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What best can be concluded about the number of offline registrations in February?
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In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months – January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
1. In every month, both online and offline registration numbers were multiples of 10.
2. In January, the number of offline registrations was twice that of online registrations.
3. In April, the number of online registrations was twice that of offline registrations.
4. The number of online registrations in March was the same as the number of offline registrations in February.
5. The number of online registrations was the largest in May.
What was the total number of registrations in April?
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What was the number of online registrations in January?
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Which of the following statements can be true?
I. The number of offline registrations was the smallest in May.
II. The total number of registrations was the smallest in February.
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What best can be concluded about the number of offline registrations in February?
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What was the total number of registrations in April?
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What was the weight of the test component?
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What was the maximum aggregate score obtained by the students?
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What was Mathew's score in the test?
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Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
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What was Rini's score in the project?
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There are only three female students – Amala, Koli and Rini – and only three male students – Biman, Mathew and Shyamal – in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1.
The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project.
The following additional facts are known about the scores in the project and the test.
1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60, respectively.
2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score.
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate.
5. Biman scored the second lowest in the test and the lowest in the aggregate.
6. Mathew scored more than Rini in the project, but less than her in the test.
What was Rini's score in the project?
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What was the weight of the test component?
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What was the maximum aggregate score obtained by the students?
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What was Mathew's score in the test?
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Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
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A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.
There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.
Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.
The following additional information is known about that day.1. All slots were full.2. The number of US applications was the same in all the slots. The same was true for the other three categories.3. 50% of the applications were US applications.4. All applicants except Ira, Vijay and Nandini arrived on time.5. Vijay was called to a counter at 9:25 am.
How many UK applications were scheduled on that day?
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There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
Step 2:
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category
So at least 2 people were scheduled for each slot for an Others category visa.
Total applications on that day = 200
US applications = 100
So there are 5 applications of US out of total 10 in one time slot.
There were 3 applications of Schengen and 2 applications of Others in 1 time slot.
Hence, there are 0 applications of UK in one time slot.
What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day?
Video Explanation
Explanatory Answer
There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
Step 2:
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category.
So at least 2 people were scheduled for each slot for an Others category visa.
Which of the following is the closest to the time when Nandini's application process got over?
Video Explanation
Explanatory Answer
There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
Step 2:
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category.
So at least 2 people were scheduled for each slot for an Others category visa.
Which of the following statements is false?
Video Explanation
Explanatory Answer
There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
Step 2:
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category.
So at least 2 people were scheduled for each slot for an Others category visa.
When did the application processing for all US applicants get over on that day?
Video Explanation
Explanatory Answer
There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category.
So at least 2 people were scheduled for each slot for an Others category visa.
How many UK applications were scheduled on that day?
Video Explanation
Explanatory Answer
There are 20 slots of 15 minutes each from 9:00 AM to 2:00 PM. There are ten counters in the VPO.
From the given information and condition (1), Total number of applications scheduled = 10 × 20 = 200
From condition (3), Number of US applications = 100. Number of application for rest 3 categories = 100.
From condition (2), Number of US applications for each slot = 100/20 = 5. Similarly, number of applications of rest 3 categories for each slot = 100/20 = 5.
The processing time for an application is the same within each category. But it may vary across the categories.
Depending on the number of applications in a category and time required to process an application for that category,
it is possible that an applicant for a slot may be processed later.
The information can be shown in the table below.
Step 2:
On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15
AM slot but entered the VPO at 9:20 AM i.e., they had delayed by 5 minutes.
So at least 3 people were scheduled for each slot for a Schengen visa.
Mahira and Osman were scheduled in the 9:30 AM slot on that day for visa processing in the Others category
So at least 2 people were scheduled for each slot for an Others category visa.
Total applications on that day = 200
US applications = 100
So there are 5 applications of US out of total 10 in one time slot.
There were 3 applications of Schengen and 2 applications of Others in 1 time slot.
Hence, there are 0 applications of UK in one time slot.
