LR - Mathematical Reasoning - Previous Year CAT/MBA Questions
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Answer the following questions based on the information given below.
Six web surfers M, N, O, P, X, and Y each had 30 stars which they distributed among four bloggers A, B, C, and D. The number of stars received by A and B from the six web surfers is shown in the figure below.
The following additional facts are known regarding the number of stars received by the
bloggers from the surfers.
1. The numbers of stars received by the bloggers from the surfers were all multiples of 5
(including 0).
2. The total numbers of stars received by the bloggers were the same.
3. Each blogger received a different number of stars from M.
4. Two surfers gave all their stars to a single blogger.
5. D received more stars than C from Y
What was the total number of stars received by D?
Solution
Discuss
ReportWhat was the number of stars received by D from Y?
- (a)
10
- (b)
0
- (c)
5
- (d)
Cannot be determined
How many surfers distributed their stars among exactly 2 bloggers?
Which of the following can be determined with certainty?
I. The number of stars received by C from M
II. The number of stars received by D from O
- (a)
Only I
- (b)
Neither I nor II
- (c)
Both I and II
- (d)
Only II
Answer the following questions based on the information given below.
Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya’s and Ramya’s campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate.
If Amiya and Ramya both run campaigns focusing on issues, then
- The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then 20 × (2+2)%, that is, 80% of the students will vote in the election.
- Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive 1/3 of the votes cast, and Ramya will receive the other 2/3. The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent.
- If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then 10% of the students who would have otherwise voted for Amiya will vote for Ramya, and another 10% who would have otherwise voted for Amiya, will not vote at all.
- If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then 20% of the students who would have otherwise voted for Ramya will vote for Amiya, and another 5% who would have otherwise voted for Ramya, will not vote at all.
- If both run campaigns attacking each other, then 10% of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.
If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?
- (a)
60%
- (b)
36%
- (c)
64%
- (d)
40%
What is the minimum percentage of students who will vote in the election?
- (a)
40%
- (b)
32%
- (c)
38%
- (d)
36%
If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she can get?
- (a)
48%
- (b)
40%
- (c)
44%
- (d)
36%
If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?
- (a)
12%
- (b)
18%
- (c)
15%
- (d)
30%
Answer the following questions based on the information given below.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.
1. Numbers in any row appear in an increasing order from left to right.
2. Numbers in any column appear in a decreasing order from top to bottom.
3. 1 is placed either in the same row or in the same column as 10.
4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
6. 4 and 6 are placed in the same row.
What is the row number which has the least sum of numbers placed in that row?
Which of the following statements MUST be true?
I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.
- (a)
Only II
- (b)
Neither I nor II
- (c)
Only I
- (d)
Both I and II
Which of the following statements MUST be true?
I. 2 is placed in a slot in Column 2.
II. 3 is placed in a slot in Column 3.
- (a)
Only II
- (b)
Neither I nor II
- (c)
Only I
- (d)
Both I and II
For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
What is the sum of the numbers placed in Column 4?
Answer the following questions based on the information given below.
An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below.
The following information is known about ratings on Day 3.
1. 100 buyers gave product ratings on Day 3.
2. The modes of the product ratings were 4 and 5.
3. The numbers of buyers giving each product rating are non-zero multiples of 10.
4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3.
How many buyers gave ratings on Day 1?
What is the daily average rating of Day 3?
- (a)
3.0
- (b)
3.5
- (c)
3.2
- (d)
3.6
What is the median of all ratings given on Day 3?
Which of the following is true about the cumulative average ratings of Day 2 and Day 3?
- (a)
The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
- (b)
The cumulative average of Day 3 increased by more than 8% from Day 2.
- (c)
The cumulative average of Day 3 decreased from Day 2.
- (d)
The cumulative average of Day 3 increased by less than 5% from Day 2.
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?
To 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?