CAT 2024 Slot 1 DILR Question & Solution
Data Set
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.
Question 1
What was the total number of stars received by D?
Solution:
We can note down the data from the chart into the form of a table, that gives us,
We are told that D receives more stars than C from Y. Considering Y has already given 25 stars, it will give 0 stars to C and 5 stars to D.
The only two surfers who have not given any stars to A or B is O and X, and these are the two surfers to give all of their stars to a single blogger.
We are also told that M gives different stars to the four bloggers,
Since he has already given 0 and 10, the remaining distinct stars should add up to 20. The only numbers that are remaining that add up to 20 are 5 and 15.
We know that X rewards one of C or D 30 stars and O rewards one of C or D 30 stars. Given that, M could not have rewarded D 15 stars, since Y rewarded D 5 stars, and D is also going to rewarded 30 stars by O or X, and since the total is same for all, which is 45. This is not possible.
This means that, M rewarded C 15 stars and D 5 stars.
This gives us two cases,
Case-1
Case-2
We can use these two cases to answer the questions,
D was rewarded 45 stars in total.
Question 2
What was the number of stars received by D from Y?
Solution:
We can note down the data from the chart into the form of a table, that gives us,
We are told that D receives more stars than C from Y. Considering Y has already given 25 stars, it will give 0 stars to C and 5 stars to D.
The only two surfers who have not given any stars to A or B is O and X, and these are the two surfers to give all of their stars to a single blogger.
We are also told that M gives different stars to the four bloggers,
Since he has already given 0 and 10, the remaining distinct stars should add up to 20. The only numbers that are remaining that add up to 20 are 5 and 15.
We know that X rewards one of C or D 30 stars and O rewards one of C or D 30 stars. Given that, M could not have rewarded D 15 stars, since Y rewarded D 5 stars, and D is also going to rewarded 30 stars by O or X, and since the total is same for all, which is 45. This is not possible.
This means that, M rewarded C 15 stars and D 5 stars.
This gives us two cases,
Case-1
Case-2
We can use these two cases to answer the questions,
D received 5 stars from Y.
Question 3
How many surfers distributed their stars among exactly 2 bloggers?
Solution:
We can note down the data from the chart into the form of a table, that gives us,
We are told that D receives more stars than C from Y. Considering Y has already given 25 stars, it will give 0 stars to C and 5 stars to D.
The only two surfers who have not given any stars to A or B is O and X, and these are the two surfers to give all of their stars to a single blogger.
We are also told that M gives different stars to the four bloggers,
Since he has already given 0 and 10, the remaining distinct stars should add up to 20. The only numbers that are remaining that add up to 20 are 5 and 15.
We know that X rewards one of C or D 30 stars and O rewards one of C or D 30 stars. Given that, M could not have rewarded D 15 stars, since Y rewarded D 5 stars, and D is also going to rewarded 30 stars by O or X, and since the total is same for all, which is 45. This is not possible.
This means that, M rewarded C 15 stars and D 5 stars.
This gives us two cases,
Case-1
Case-2
We can use these two cases to answer the questions,
M distributed among 3 bloggers, N among 2 bloggers, O among 1, P among 2, X among 1, Y among 3
Hence 2 surfers distribute their stars among 2 bloggers.
Question 4
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
Solution:
We can note down the data from the chart into the form of a table, that gives us,
We are told that D receives more stars than C from Y. Considering Y has already given 25 stars, it will give 0 stars to C and 5 stars to D.
The only two surfers who have not given any stars to A or B is O and X, and these are the two surfers to give all of their stars to a single blogger.
We are also told that M gives different stars to the four bloggers,
Since he has already given 0 and 10, the remaining distinct stars should add up to 20. The only numbers that are remaining that add up to 20 are 5 and 15.
We know that X rewards one of C or D 30 stars and O rewards one of C or D 30 stars. Given that, M could not have rewarded D 15 stars, since Y rewarded D 5 stars, and D is also going to rewarded 30 stars by O or X, and since the total is same for all, which is 45. This is not possible.
This means that, M rewarded C 15 stars and D 5 stars.
This gives us two cases,
Case-1
Case-2
We can use these two cases to answer the questions,
There are two cases formed since we cannot identify for certain two whom did O reward the stars to,
We can identify the number of stars rewarded by M to C.
Hence only statement 1 can be identified uniquely.