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In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?
- a)11:1
- b)6:1
- c)11:2
- d)4:1
- e)3:1
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a certain class, all the students like at least one of the followin...
Given:
- Percentage of students who like Game of Thrones = 55%
- Percentage of students who like Friends = 86%
- Percentage of students who like Big Bang Theory = 69%
Let's assume that there are 100 students in the class.
Understanding the problem:
- All the students in the class like at least one of the three TV shows.
- We need to find the ratio of the maximum to the minimum value of x, where x is the percentage of students who like all three TV shows.
Solution:
Step 1: Find the number of students who like each TV show.
- Number of students who like Game of Thrones = 55% of 100 = 55
- Number of students who like Friends = 86% of 100 = 86
- Number of students who like Big Bang Theory = 69% of 100 = 69
Step 2: Represent the number of students who like each TV show using a Venn diagram.
Let's represent the number of students who like Game of Thrones, Friends, and Big Bang Theory as follows:
```
Game of Thrones
(55 students)
/ \
/ \
/ \
/ \
Friends (86 students) Big Bang Theory (69 students)
```
Step 3: Calculate the minimum value of x.
The minimum value of x occurs when there is no overlap between the three TV shows.
So, the minimum value of x = 0%.
Step 4: Calculate the maximum value of x.
The maximum value of x occurs when all the students who like Game of Thrones, Friends, and Big Bang Theory also like all three TV shows.
From the Venn diagram, it can be observed that the maximum number of students who like all three TV shows is the smallest number among Game of Thrones, Friends, and Big Bang Theory.
So, the maximum value of x = (smallest number / total number of students) * 100.
In this case, the smallest number is 55 (students who like Game of Thrones).
Therefore, the maximum value of x = (55 / 100) * 100 = 55%.
Step 5: Calculate the ratio of the maximum to the minimum value of x.
Ratio = maximum value of x / minimum value of x = 55% / 0% = Not defined
Conclusion:
The ratio of the maximum to the minimum value of x is not defined because the minimum value of x is 0%.
- Percentage of students who like Game of Thrones = 55%
- Percentage of students who like Friends = 86%
- Percentage of students who like Big Bang Theory = 69%
Let's assume that there are 100 students in the class.
Understanding the problem:
- All the students in the class like at least one of the three TV shows.
- We need to find the ratio of the maximum to the minimum value of x, where x is the percentage of students who like all three TV shows.
Solution:
Step 1: Find the number of students who like each TV show.
- Number of students who like Game of Thrones = 55% of 100 = 55
- Number of students who like Friends = 86% of 100 = 86
- Number of students who like Big Bang Theory = 69% of 100 = 69
Step 2: Represent the number of students who like each TV show using a Venn diagram.
Let's represent the number of students who like Game of Thrones, Friends, and Big Bang Theory as follows:
```
Game of Thrones
(55 students)
/ \
/ \
/ \
/ \
Friends (86 students) Big Bang Theory (69 students)
```
Step 3: Calculate the minimum value of x.
The minimum value of x occurs when there is no overlap between the three TV shows.
So, the minimum value of x = 0%.
Step 4: Calculate the maximum value of x.
The maximum value of x occurs when all the students who like Game of Thrones, Friends, and Big Bang Theory also like all three TV shows.
From the Venn diagram, it can be observed that the maximum number of students who like all three TV shows is the smallest number among Game of Thrones, Friends, and Big Bang Theory.
So, the maximum value of x = (smallest number / total number of students) * 100.
In this case, the smallest number is 55 (students who like Game of Thrones).
Therefore, the maximum value of x = (55 / 100) * 100 = 55%.
Step 5: Calculate the ratio of the maximum to the minimum value of x.
Ratio = maximum value of x / minimum value of x = 55% / 0% = Not defined
Conclusion:
The ratio of the maximum to the minimum value of x is not defined because the minimum value of x is 0%.
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Community Answer
In a certain class, all the students like at least one of the followin...
Maximum Value
All = GOT + F + BBT - only GOT&F - only F&BBT - only GOT&BBT - 2 (GOT&F&BBT) + Neither
100 = 55 + 86 + 69 - only 2 - 2 (all 3) + 0
Only 2 + 2 (all 3) = 210 - 100
To maximise all 3, only 2 be 0
2 (all 3) = 110
all 3 = 55, which is equal to the min value of all 3 so it is possible
Minimum Value
Minimum Value of x means minimum overlap of all 3
That means max separation of all the sub-sets
That means max separation of all the sub-sets
So % of students not liking GOT = 45
% of students not liking F = 14
% of students not liking BBT = 31
% of students not liking F = 14
% of students not liking BBT = 31
% of students liking all 3 = 100 - 45 -14 -31 = 10
Alternatively, make a Venn diagram and try to fit the lowest value i.e. GOT (55) in the portion of only F and only BBT, the balance which cannot be placed goes into the 'all 3' portion. Same result, all 3 = 10
Ratio = 55/10
= 11/2
= 11/2
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In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer?
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In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer?.
In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a certain class, all the students like at least one of the following TV shows: Game of Thrones, Friends, and Big Bang Theory. It was found that the percentage of students who like the shows are 55, 86, and 69 respectively. If x% of the students in the class like all three TV shows, what is the ratio of the maximum to the minimum value of x?a)11:1b)6:1c)11:2d)4:1e)3:1Correct answer is option 'C'. Can you explain this answer?.
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