CAT — Bar Graphs
24 questions, free to view. Click any question to see the answer and explanation.
Answer the questions on the basis of the information given below.
Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii) Elder, and iii) Others.
Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the 'Kid' and 'Elder' categories.
The following additional facts are known about the numbers of subscribers.
1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the 'Kid' category and 2/3 of the subscribers from the 'Elder' category subscribers use one app.
3. In 2023, the number of subscribers from the 'Kid' category who used multiple apps was the same as the number of subscribers from the 'Elder' category who used one app.
4. 10,000 subscribers from the 'Kid' category used one app and 15,000 subscribers from the 'Elder' category used multiple apps in 2023.
How many subscribers belonged to the 'Others' category in 2024?
45000
65000
55000
Cannot be determined
55000
Step 1:
From condition (4), the number of kids using one app in 2023 is 10,000, while the number of elders using multiple apps is 15,000.
According to condition (3), the number of elders using one app is equal to the number of kids using multiple apps. Let this common value be X.
From the graph, in 2023, kids account for 15% of the users and elders account for 20%. Therefore, the remaining 65% correspond to others.
Using this information,
(10000 + X) / (15000 + X) = 15 / 20
⇒ X = 5000
Hence,
- Kids (2023) = 10,000 + 5,000 = 15,000
- Elders (2023) = 5,000 + 15,000 = 20,000
- Others (2023) = 65,000
Thus, the total number of users in 2023 is:
15,000 + 20,000 + 65,000 = 100,000
From condition (1), the total number of users in 2024 is 10% higher than in 2023.
Therefore,
Total users in 2024 = 100,000 × 1.10 = 110,000
Using the bar graph, the category-wise totals for 2024 are:
- Kids = 22,000
- Elders = 33,000
- Others = 55,000
The complete values are:
2023
- Kids: One app = 10,000, Multiple apps = 5,000, Total = 15,000
- Elders: One app = 5,000, Multiple apps = 15,000, Total = 20,000
- Others: Total = 65,000
- Overall total = 100,000
2024
- Kids: One app = 11,000, Multiple apps = 11,000, Total = 22,000
- Elders: One app = 22,000, Multiple apps = 11,000, Total = 33,000
- Others: Total = 55,000
- Overall total = 110,000
In 2024 the number of people in others category = 55000.
What percentage of subscribers in the 'Kid' category used multiple apps in 2023?
33.33%
50.00%
5.00%
25.50%
33.33%
Step 1:
From condition (4), the number of kids using one app in 2023 is 10,000, while the number of elders using multiple apps is 15,000.
According to condition (3), the number of elders using one app is equal to the number of kids using multiple apps. Let this common value be X.
From the graph, in 2023, kids account for 15% of the users and elders account for 20%. Therefore, the remaining 65% correspond to others.
Using this information,
(10000 + X) / (15000 + X) = 15 / 20
⇒ X = 5000
Hence,
- Kids (2023) = 10,000 + 5,000 = 15,000
- Elders (2023) = 5,000 + 15,000 = 20,000
- Others (2023) = 65,000
Thus, the total number of users in 2023 is:
15,000 + 20,000 + 65,000 = 100,000
From condition (1), the total number of users in 2024 is 10% higher than in 2023.
Therefore,
Total users in 2024 = 100,000 × 1.10 = 110,000
Using the bar graph, the category-wise totals for 2024 are:
- Kids = 22,000
- Elders = 33,000
- Others = 55,000
The complete values are:
2023
- Kids: One app = 10,000, Multiple apps = 5,000, Total = 15,000
- Elders: One app = 5,000, Multiple apps = 15,000, Total = 20,000
- Others: Total = 65,000
- Overall total = 100,000
2024
- Kids: One app = 11,000, Multiple apps = 11,000, Total = 22,000
- Elders: One app = 22,000, Multiple apps = 11,000, Total = 33,000
- Others: Total = 55,000
- Overall total = 110,000
The percentage of kids using multiple apps in 2023 is:
= (5000 / 15000) × 100
= 33.33%
What was the percentage increase in the number of subscribers in the 'Elder' category from 2023 to 2024?
60%
50%
65%
40%
Step 1:
From condition (4), the number of kids using one app in 2023 is 10,000, while the number of elders using multiple apps is 15,000.
According to condition (3), the number of elders using one app is equal to the number of kids using multiple apps. Let this common value be X.
From the graph, in 2023, kids account for 15% of the users and elders account for 20%. Therefore, the remaining 65% correspond to others.
Using this information,
(10000 + X) / (15000 + X) = 15 / 20
⇒ X = 5000
Hence,
- Kids (2023) = 10,000 + 5,000 = 15,000
- Elders (2023) = 5,000 + 15,000 = 20,000
- Others (2023) = 65,000
Thus, the total number of users in 2023 is:
15,000 + 20,000 + 65,000 = 100,000
From condition (1), the total number of users in 2024 is 10% higher than in 2023.
Therefore,
Total users in 2024 = 100,000 × 1.10 = 110,000
Using the bar graph, the category-wise totals for 2024 are:
- Kids = 22,000
- Elders = 33,000
- Others = 55,000
The complete values are:
2023
- Kids: One app = 10,000, Multiple apps = 5,000, Total = 15,000
- Elders: One app = 5,000, Multiple apps = 15,000, Total = 20,000
- Others: Total = 65,000
- Overall total = 100,000
2024
- Kids: One app = 11,000, Multiple apps = 11,000, Total = 22,000
- Elders: One app = 22,000, Multiple apps = 11,000, Total = 33,000
- Others: Total = 55,000
- Overall total = 110,000
The percentage increase in the number of elders from 2023 to 2024 is:
= ((33,000 − 20,000) / 20,000) × 100
= 65%
What could be the minimum percentage of subscribers who used multiple apps in 2024?
20.0%
10.0%
16.5%
22.00%
20.0%
Step 1:
From condition (4), the number of kids using one app in 2023 is 10,000, while the number of elders using multiple apps is 15,000.
According to condition (3), the number of elders using one app is equal to the number of kids using multiple apps. Let this common value be X.
From the graph, in 2023, kids account for 15% of the users and elders account for 20%. Therefore, the remaining 65% correspond to others.
Using this information,
(10000 + X) / (15000 + X) = 15 / 20
⇒ X = 5000
Hence,
- Kids (2023) = 10,000 + 5,000 = 15,000
- Elders (2023) = 5,000 + 15,000 = 20,000
- Others (2023) = 65,000
Thus, the total number of users in 2023 is:
15,000 + 20,000 + 65,000 = 100,000
From condition (1), the total number of users in 2024 is 10% higher than in 2023.
Therefore,
Total users in 2024 = 100,000 × 1.10 = 110,000
Using the bar graph, the category-wise totals for 2024 are:
- Kids = 22,000
- Elders = 33,000
- Others = 55,000
The complete values are:
2023
- Kids: One app = 10,000, Multiple apps = 5,000, Total = 15,000
- Elders: One app = 5,000, Multiple apps = 15,000, Total = 20,000
- Others: Total = 65,000
- Overall total = 100,000
2024
- Kids: One app = 11,000, Multiple apps = 11,000, Total = 22,000
- Elders: One app = 22,000, Multiple apps = 11,000, Total = 33,000
- Others: Total = 55,000
- Overall total = 110,000
The minimum number of people using multiple apps in 2024 is:
= 11,000 + 11,000 + 0
= 22,000
Therefore, the required percentage is:
= (22,000 / 110,000) × 100
= 20%
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?
3.2
3.5
3.0
3.6
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?
The cumulative average of Day 3 decreased from Day 2.
The cumulative average of Day 3 increased by more than 8% from Day 2.
The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
The cumulative average of Day 3 increased by less than 5% from Day 2.
The cumulative average of Day 3 increased by a percentage between 5% and 8% from Day 2.
The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.
The following additional facts are known.
1. Each of the authors wrote at least one of each of the four types of papers.
2. The four authors wrote different numbers of single-author papers.
3. Both Chintan and Devon wrote more three-author papers than Brajen.
4. The number of single-author and two-author papers written by Brajen were the same.
What was the total number of two-author and threeauthor papers written by Brajen?
Step 1:
From the first bar graph, we know the total number of titles authored by each individual. We are also given the total number of single-author, two-author, three-author, and four-author papers.
Observe that 2 four-author papers contribute 2 × 4 = 8 author counts, since all four authors are involved in each paper. The same counting principle applies to the three-author and two-author papers.
Using Condition (1), each author contributed to at least one paper of every type. Therefore, none of the entries in the table can be 0.
Since Aman has authored 5 papers in total, and 2 of them are four-author papers, the remaining 3 papers must be distributed among the other three categories. As every category must have at least one paper, Aman must have 1 single-author, 1 two-author, and 1 three-author paper.
From Condition (2), every author has a distinct number of single-author papers. Since Aman already has 1, the remaining authors must have 2, 3, and 4 single-author papers.
Step 2:
Using Condition (4), Brajen cannot have 4 single-author and two-author papers combined, because the overall total for these categories is 8. He also cannot have 3, as that would leave him with 0 three-author papers, violating the given conditions.
Hence, Brajen must have 2 single-author papers and 2 two-author papers. Since his total is 8, he must also have 2 three-author papers.
Now, applying Condition (3), both Chintan and Devon must have more than 2 three-author papers, and the total number of three-author papers contributed by all authors is 9. The only feasible allocation is 3 each for Chintan and Devon.
The deductions obtained so far are summarized in the table below.
Therefore, the total number of two-author and three-author papers written by Brajen is:
2 + 2 = 4.
Which of the following statements is/are NECESSARILY true?
i. Chintan wrote exactly three two-author papers.
ii. Chintan wrote more single-author papers than Devon.
Neither i nor ii
Only i
Both i and ii
Only ii
Neither i nor ii
Step 1:
From the first bar graph, we know the total number of titles authored by each individual. We are also given the total number of single-author, two-author, three-author, and four-author papers.
Observe that 2 four-author papers contribute 2 × 4 = 8 author counts, since all four authors are involved in each paper. The same counting principle applies to the three-author and two-author papers.
Using Condition (1), each author contributed to at least one paper of every type. Therefore, none of the entries in the table can be 0.
Since Aman has authored 5 papers in total, and 2 of them are four-author papers, the remaining 3 papers must be distributed among the other three categories. As every category must have at least one paper, Aman must have 1 single-author, 1 two-author, and 1 three-author paper.
From Condition (2), every author has a distinct number of single-author papers. Since Aman already has 1, the remaining authors must have 2, 3, and 4 single-author papers.
Step 2:
Using Condition (4), Brajen cannot have 4 single-author and two-author papers combined, because the overall total for these categories is 8. He also cannot have 3, as that would leave him with 0 three-author papers, violating the given conditions.
Hence, Brajen must have 2 single-author papers and 2 two-author papers. Since his total is 8, he must also have 2 three-author papers.
Now, applying Condition (3), both Chintan and Devon must have more than 2 three-author papers, and the total number of three-author papers contributed by all authors is 9. The only feasible allocation is 3 each for Chintan and Devon.
The deductions obtained so far are summarized in the table below.
Let us check each statement:
i. The statement, Chintan wrote exactly three two-author papers may not necessarily be true.
ii. The statement, Chintan wrote more single-author papers than Devon may not necessarily be true.
Hence, neither i nor ii is definitely true.
Which of the following statements is/are NECESSARILY true?
i. Arman wrote three-author papers only with Chintan and Devon.
ii. Brajen wrote three-author papers only with Chintan and Devon.
Neither i or ii
Both i and ii
Only ii
Only i
Both i and ii
Step 1:
From the first bar graph, we know the total number of titles authored by each individual. We are also given the total number of single-author, two-author, three-author, and four-author papers.
Observe that 2 four-author papers contribute 2 × 4 = 8 author counts, since all four authors are involved in each paper. The same counting principle applies to the three-author and two-author papers.
Using Condition (1), each author contributed to at least one paper of every type. Therefore, none of the entries in the table can be 0.
Since Aman has authored 5 papers in total, and 2 of them are four-author papers, the remaining 3 papers must be distributed among the other three categories. As every category must have at least one paper, Aman must have 1 single-author, 1 two-author, and 1 three-author paper.
From Condition (2), every author has a distinct number of single-author papers. Since Aman already has 1, the remaining authors must have 2, 3, and 4 single-author papers.
Step 2:
Using Condition (4), Brajen cannot have 4 single-author and two-author papers combined, because the overall total for these categories is 8. He also cannot have 3, as that would leave him with 0 three-author papers, violating the given conditions.
Hence, Brajen must have 2 single-author papers and 2 two-author papers. Since his total is 8, he must also have 2 three-author papers.
Now, applying Condition (3), both Chintan and Devon must have more than 2 three-author papers, and the total number of three-author papers contributed by all authors is 9. The only feasible allocation is 3 each for Chintan and Devon.
The deductions obtained so far are summarized in the table below.
There are 3 three author papers and both Chintan and Devon wrote 3 three author papers whereas Aman wrote 1 and Brajen wrote 2. So the only possible combination will be {(Chintan, Devon, Aman), (Chintan, Devon, Brajen), (Chintan, Devon, Brajen)}. Hence, the statement, Arman wrote three-author papers only with Chintan and Devon, is true. Brajen wrote three-author papers only with Chintan and Devon is also true. Hence, both (i) and (ii) are true.
If Devon wrote more than one two-author papers, then how many two-author papers did Chintan write?
Step 1:
From the first bar graph, we know the total number of titles authored by each individual. We are also given the total number of single-author, two-author, three-author, and four-author papers.
Observe that 2 four-author papers contribute 2 × 4 = 8 author counts, since all four authors are involved in each paper. The same counting principle applies to the three-author and two-author papers.
Using Condition (1), each author contributed to at least one paper of every type. Therefore, none of the entries in the table can be 0.
Since Aman has authored 5 papers in total, and 2 of them are four-author papers, the remaining 3 papers must be distributed among the other three categories. As every category must have at least one paper, Aman must have 1 single-author, 1 two-author, and 1 three-author paper.
From Condition (2), every author has a distinct number of single-author papers. Since Aman already has 1, the remaining authors must have 2, 3, and 4 single-author papers.
Step 2:
Using Condition (4), Brajen cannot have 4 single-author and two-author papers combined, because the overall total for these categories is 8. He also cannot have 3, as that would leave him with 0 three-author papers, violating the given conditions.
Hence, Brajen must have 2 single-author papers and 2 two-author papers. Since his total is 8, he must also have 2 three-author papers.
Now, applying Condition (3), both Chintan and Devon must have more than 2 three-author papers, and the total number of three-author papers contributed by all authors is 9. The only feasible allocation is 3 each for Chintan and Devon.
The deductions obtained so far are summarized in the table below.
If Devon wrote more than one two-author papers, then the number of two-author papers written by Chintan is 3.
Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others.
For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.
Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows.
Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y.
A negative trade surplus is called trade deficit.
How much is Japan’s export to India worth?
7.0 Billion USD
1.75 Billion USD
16.0 Billion USD
8.5 Billion USD
7.0 Billion USD
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
India charged an import tariff of 3.5 billion USD on imports from Japan, which is 50% of the total imports. Hence, Japan’s exports to India are worth 7.0 billion USD.
Which among the following is the highest?
Exports by Japan to UK
Exports by France to Japan
Imports by France from India
Imports by US from France
Imports by US from France
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Option (1): Exports by Japan to UK = 6 × 1/0.4 = 15 Billion USD
Option (2): Exports by France to Japan = 3 × 1/ 0.3 = 10 Billion USD
Option (3): Imports by France from India = 6.5 × 1/ 0.4 = 16.25 Billion USD
Option (4): Imports by US from France = 6 × 1/0.2 = 30 Billion USD
Hence, option (4) is the correct answer.
What is the trade surplus/trade deficit of India with UK?
Deficit of 15.0 Billion USD
Surplus of 15.0 Billion USD
Surplus of 10.0 Billion USD
Deficit of 10.0 Billion USD
Deficit of 15.0 Billion USD
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Import by India from UK = 5 × 1/0.2 = 25 Billion USD
Export from India to UK = 3 × 1/0.3 = 10 Billion USD
Hence, trade deficit of India with UK = 25 – 10 = 15 Billion USD
Among France and UK, who has/have trade surplus(es) with US?
Both France and UK
Only UK
Neither France nor UK
Only France
Only France
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Import by France from US = 5.5 × 1/0.3 = 18.33 Billion USD
Export by France to US = 6 × 1/0.2 = 30 Billion USD
So trade surplus of France with US = 30 – 18.33 = 11.66 Billion USD
Import by UK from US = 2.5 × 1/0.2 = 12.5 Billion USD
Export from UK to US = 3 × 1/0.3 = 10 Billion USD
So trade deficit of UK with US = 12.5 – 10 = 2.5 Billion USD
Hence, only France has trade surplus with US.
The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).
The following additional facts are known about the countries visited by them.
1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh?
How many countries in Europe were visited only by Nitesh?
How many countries in the ROW were visited by both Nitesh and Samantha?
How many countries in Europe were visited by exactly one of Dheeraj, Samantha and Nitesh?
14
12
5
10
12
The number of countries in Europe that were visited by exactly one of Dheeraj, Samantha, and Nitesh = 6 + 2 + 4 = 12.
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?
Common Solution:
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
What was the number of stars received by D from Y?
10
5
0
cannot be determined
5
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
How many surfers distributed their stars among exactly 2 bloggers?
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
Which of the following can be determined with certainty?
I. The numbers of stars received by C from M
II. The number of stars received by D from O
Only I
Only II
Both I and II
Neither I nor II
Only I
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
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