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A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.
Q. Which of the following is not possible?
- a)There are exactly 75 items of type e.
- b)There are exactly 30 items of type b
- c)There are exactly 45 items of type c.
- d)There are exactly 60 items of type d.
Correct answer is option 'C'. Can you explain this answer?
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A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a r...
Option A: There are exactly 75 items of type e.
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a=1,b=2,c=4,d=8, e=85. Here the maximum value of e= 85. Hence it can take the value 75.
An example of such case is a=1,b=2,c=4,d=18, e=75
Option B: There are exactly 30 items of type b. a=1 b=30 and c=69. Hence this case is also possible.
Option C: There are exactly 45 items of type c.
Since the value of d should be at least 90, it means that d is not present because 45+90 will be more than 100(maximum number of items). Only a,b and c are present.
The maximum value of b = 22 and a =1, but 45+22+1=68, which is less than 100. So this case is not possible.
Option D: There are exactly 60 items of type d.
d=60, c=30, b=9 and a=1. a+b+c+d=100. Hence this case is possible.
C is the answer.
Most Upvoted Answer
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a r...
Understanding the Prize Distribution
In this game show, the distribution of prizes follows a specific pattern based on their types and values. The key points to remember are:
- There is 1 diamond ring (type a).
- The number of items doubles with each subsequent type:
- Type b: At least 2 items
- Type c: At least 4 items
- Type d: At least 8 items
- Type e: At least 16 items
Analyzing the Options
Let's evaluate each option to see if it conforms to the doubling rule:
Conclusion
The only option that does not adhere to the game’s rules regarding the distribution of prizes is option c, which states 45 items of type c. This violates the doubling principle while exceeding the available boxes.
In this game show, the distribution of prizes follows a specific pattern based on their types and values. The key points to remember are:
- There is 1 diamond ring (type a).
- The number of items doubles with each subsequent type:
- Type b: At least 2 items
- Type c: At least 4 items
- Type d: At least 8 items
- Type e: At least 16 items
Analyzing the Options
Let's evaluate each option to see if it conforms to the doubling rule:
- a) 75 items of type e: This is possible. If there are 75 items of type e, it can support 37 items of type d, 18 items of type c, 9 items of type b, and 4 items of type a (doubling down). Thus, this scenario is valid.
- b) 30 items of type b: This is also possible. If there are 30 items of type b, there must be at least 60 items of type c. This distribution still adheres to the doubling rule and is feasible.
- c) 45 items of type c: This is not possible. If there are 45 items of type c, there must be at least 90 items of type b (double of c). This exceeds the total available boxes (100). Therefore, this option violates the constraints.
- d) 60 items of type d: This is possible. If there are 60 items of type d, that allows for 120 items of type e, which is not feasible within the 100 boxes, but if we scale back appropriately, we can adjust the counts of types c and b to fit.
Conclusion
The only option that does not adhere to the game’s rules regarding the distribution of prizes is option c, which states 45 items of type c. This violates the doubling principle while exceeding the available boxes.
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A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer?
Question Description
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer?.
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer?.
Solutions for A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.Q. Which of the following is not possible?a) There are exactly 75 items of type e.b) There are exactly 30 items of type bc) There are exactly 45 items of type c.d) There are exactly 60 items of type d.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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