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Instructions
Comprehension:
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. What is the maximum possible number of different types of prizes?
Comprehension:
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. What is the maximum possible number of different types of prizes?
Correct answer is '6'. Can you explain this answer?
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Verified Answer
InstructionsComprehension:A new game show on TV has 100 boxes numbered...
It is given that the most expensive item is a diamond ring of type a and there is exactly one of these. Since the number of items of type b should be at least twice of that of a and the number of items of type c should be at least twice of that of b and so on. So the maximum number of different types of items of a, b and c will be obtained when a=1, b=2, c=4, d=8, e=16, f=69. Hence the maximum number of different types of items will be 6.
If the number of items is 7, then the minimum number of prizes should be 1+2+4+8+16+32+64=127 which is more than 100.
Hence 6 is the answer.
If the number of items is 7, then the minimum number of prizes should be 1+2+4+8+16+32+64=127 which is more than 100.
Hence 6 is the answer.
Most Upvoted Answer
InstructionsComprehension:A new game show on TV has 100 boxes numbered...
Maximum Number of Different Types of Prizes
The maximum possible number of different types of prizes in the game show can be determined by considering the doubling rule given in the question.
Diamond Ring (Type a)
- There is exactly one diamond ring, which is the most expensive item.
Type b Prizes
- As per the doubling rule, there must be at least twice as many items of type b as of type a.
- Therefore, there can be a maximum of 2 prizes of type b.
Type c Prizes
- Similarly, there must be at least twice as many items of type c as of type b.
- Therefore, there can be a maximum of 4 prizes of type c.
Type d Prizes
- Following the doubling rule, there can be a maximum of 8 prizes of type d.
Type e Prizes
- By continuing this pattern, there can be a maximum of 16 prizes of type e.
Type f Prizes
- Finally, there can be a maximum of 32 prizes of type f.
Therefore, considering the doubling rule and the maximum number of each type of prize, the total number of different types of prizes is 6, with a, b, c, d, e, and f being the possible types of prizes in the game show.
The maximum possible number of different types of prizes in the game show can be determined by considering the doubling rule given in the question.
Diamond Ring (Type a)
- There is exactly one diamond ring, which is the most expensive item.
Type b Prizes
- As per the doubling rule, there must be at least twice as many items of type b as of type a.
- Therefore, there can be a maximum of 2 prizes of type b.
Type c Prizes
- Similarly, there must be at least twice as many items of type c as of type b.
- Therefore, there can be a maximum of 4 prizes of type c.
Type d Prizes
- Following the doubling rule, there can be a maximum of 8 prizes of type d.
Type e Prizes
- By continuing this pattern, there can be a maximum of 16 prizes of type e.
Type f Prizes
- Finally, there can be a maximum of 32 prizes of type f.
Therefore, considering the doubling rule and the maximum number of each type of prize, the total number of different types of prizes is 6, with a, b, c, d, e, and f being the possible types of prizes in the game show.
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Community Answer
InstructionsComprehension:A new game show on TV has 100 boxes numbered...
- It is given that the most expensive item is a diamond ring of type a and there is exactly one of these. Since the number of items of type b should be at least twice of that of a and the number of items of type c should be at least twice of that of b and so on.
- So the maximum number of different types of items of a, b and c will be obtained when a=1, b=2, c=4, d=8, e=16, f=69. Hence the maximum number of different types of items will be 6.
- If the number of items is 7, then the minimum number of prizes should be 1+2+4+8+16+32+64=127 which is more than 100.
Hence 6 is the answer.
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InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer?
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InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. 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 InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer?.
InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. 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 InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer?.
Solutions for InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer?, a detailed solution for InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? has been provided alongside types of InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice InstructionsComprehension: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.What is the maximum possible number of different types of prizes?Correct answer is '6'. Can you explain this answer? tests, examples and also practice CAT tests.
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