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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. 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
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a r...
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.
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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
A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a r...
Because minimum we have go take twice of each gift that is 1 2 4 8 16 32, next can't be 64 as it will be more than 100 so 1 2 4 8 16 69
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A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a r...
Introduction:
In this game show, there are 100 boxes numbered from 1 to 100, each containing a mystery prize. The prizes are of different types, denoted as a, b, c, and so on, in decreasing order of value. The most valuable item is a diamond ring, which is of type a, and there is exactly one of these. The number of items at least doubles as we move to the next type, i.e., there are 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. We are required to determine the maximum possible number of different types of prizes.
Solution:
To find the maximum possible number of different types of prizes, we need to determine the minimum number of items for each type such that the doubling condition is satisfied.
Step 1: Determining the number of items for type a (diamond ring):
Since there is exactly one diamond ring, there can be no other prizes of type a. Therefore, the number of items for type a is 1.
Step 2: Determining the number of items for type b:
To satisfy the doubling condition, there must be at least twice as many items of type b as of type a. Since there is only one item of type a, there must be a minimum of 2 items of type b.
Step 3: Determining the number of items for type c:
Similarly, there must be at least twice as many items of type c as of type b. Since we have a minimum of 2 items of type b, there must be a minimum of 4 items of type c.
Step 4: Determining the number of items for type d:
Again, there must be at least twice as many items of type d as of type c. Since we have a minimum of 4 items of type c, there must be a minimum of 8 items of type d.
Step 5: Determining the number of items for type e:
Following the doubling condition, there must be at least twice as many items of type e as of type d. Since we have a minimum of 8 items of type d, there must be a minimum of 16 items of type e.
Step 6: Determining the number of items for type f:
Continuing with the doubling condition, there must be at least twice as many items of type f as of type e. Since we have a minimum of 16 items of type e, there must be a minimum of 32 items of type f.
Step 7: Determining the number of items for type g:
Applying the doubling condition, there must be at least twice as many items of type g as of type f. Since we have a minimum of 32 items of type f, there must be a minimum of 64 items of type g.
Step 8: Determining the number of items for type h:
Following the doubling condition, there must be at least twice as many items of type h as of type g. Since we have a minimum of 64 items of type g, there must be a minimum of 128 items of type h.
Step 9:
In this game show, there are 100 boxes numbered from 1 to 100, each containing a mystery prize. The prizes are of different types, denoted as a, b, c, and so on, in decreasing order of value. The most valuable item is a diamond ring, which is of type a, and there is exactly one of these. The number of items at least doubles as we move to the next type, i.e., there are 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. We are required to determine the maximum possible number of different types of prizes.
Solution:
To find the maximum possible number of different types of prizes, we need to determine the minimum number of items for each type such that the doubling condition is satisfied.
Step 1: Determining the number of items for type a (diamond ring):
Since there is exactly one diamond ring, there can be no other prizes of type a. Therefore, the number of items for type a is 1.
Step 2: Determining the number of items for type b:
To satisfy the doubling condition, there must be at least twice as many items of type b as of type a. Since there is only one item of type a, there must be a minimum of 2 items of type b.
Step 3: Determining the number of items for type c:
Similarly, there must be at least twice as many items of type c as of type b. Since we have a minimum of 2 items of type b, there must be a minimum of 4 items of type c.
Step 4: Determining the number of items for type d:
Again, there must be at least twice as many items of type d as of type c. Since we have a minimum of 4 items of type c, there must be a minimum of 8 items of type d.
Step 5: Determining the number of items for type e:
Following the doubling condition, there must be at least twice as many items of type e as of type d. Since we have a minimum of 8 items of type d, there must be a minimum of 16 items of type e.
Step 6: Determining the number of items for type f:
Continuing with the doubling condition, there must be at least twice as many items of type f as of type e. Since we have a minimum of 16 items of type e, there must be a minimum of 32 items of type f.
Step 7: Determining the number of items for type g:
Applying the doubling condition, there must be at least twice as many items of type g as of type f. Since we have a minimum of 32 items of type f, there must be a minimum of 64 items of type g.
Step 8: Determining the number of items for type h:
Following the doubling condition, there must be at least twice as many items of type h as of type g. Since we have a minimum of 64 items of type g, there must be a minimum of 128 items of type h.
Step 9:
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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. What is the maximum possible number of different types of prizes?Correct answer is '6'. 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. 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 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 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 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 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 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 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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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 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 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 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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