LR - Mathematical Reasoning - Previous Year CAT/MBA Questions
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Answer the following questions based on the information given below:
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5.
The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively.
The summary statistics of these ratings for the five workers is given below.
* Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker.
The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers.
(a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu.
(b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
How many individual ratings cannot be determined from the above information?
Solution
Discuss
ReportTo how many workers did R2 give a rating of 4?
What rating did R1 give to Xavier?
What is the median of the ratings given by R3 to the five workers?
Which among the following restaurants gave its median rating to exactly one of the workers?
- (a)
R5
- (b)
R4
- (c)
R2
- (d)
R3
Answer the following questions based on the information given below:
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
For which firm(s) can the amounts raised by them be concluded with certainty in each year?
- (a)
Only Czechy
- (b)
Only Bzygoo and Czechy and Drjbna
- (c)
Only Drjbna
- (d)
Only Czechy and Drjbna
What best can be concluded about the total amount of money raised in 2015?
- (a)
It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
- (b)
It is either Rs. 7 crores or Rs. 8 crores.
- (c)
It is exactly Rs. 8 crores.
- (d)
It is either Rs. 8 crores or Rs. 9 crores.
What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013?
If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?
- (a)
10
- (b)
9
- (c)
12
- (d)
11
If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?
- (a)
Alfloo raised the same amount of money as Drjbna in 2013.
- (b)
Bzygoo raised more money than Elavalaki in 2014.
- (c)
Bzygoo raised the same amount of money as Elavalaki in 2013.
- (d)
Alfloo raised the same amount of money as Bzygoo in 2014.
Answer the following questions based on the information given below:
Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for
Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2.
The following information is also known.
- Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4.
- The total score on Day 3 is the same as the total score on Day 4.
- Bimal’s scores are the same on Day 1 and Day 3.
What is Akhil's score on Day 1?
- (a)
7
- (b)
6
- (c)
5
- (d)
8
Who attains the maximum total score?
- (a)
Bimal
- (b)
Chatur
- (c)
Cannot be determined
- (d)
Akhil
What is the minimum possible total score of Bimal?
If Akhil attains a total score of 24, then what is the total score of Bimal?
Answer the following questions based on the information given below:
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?
What was the number of online registrations in January?
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.
- (a)
Only II
- (b)
Only I
- (c)
Both I and II
- (d)
Neither I nor II
What best can be concluded about the number of offline registrations in February?
- (a)
50
- (b)
30 or 50 or 80
- (c)
50 or 80
- (d)
80
Which pair of months definitely had the same total number of registrations?
I. January and April
II. February and May
- (a)
Neither I nor II
- (b)
Only II
- (c)
Only I
- (d)
Both I and II
Answer the following questions based on the information given below:
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?
What was the weight of the test component?
- (a)
0.75
- (b)
0.60
- (c)
0.40
- (d)
0.50
What was the maximum aggregate score obtained by the students?
- (a)
66
- (b)
80
- (c)
62
- (d)
68
What was Mathew’s score in the test?
Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
- (a)
Neither i) nor ii)
- (b)
Only ii)
- (c)
Only i)
- (d)
Both i) and ii)
Answer the next 5 questions based on the information given below:
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only.
Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.
Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.
The following additional facts are known:
1. Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.
2. Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.
3. Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.
How many tokens did Qahira receive?
