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.
Question: 1
What is the minimum possible number of different types of prizes?
What is the minimum possible number of different types of prizes?
Updated On: Jul 8, 2024
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Correct Answer: 2
Solution and Explanation
The minimum possible number of different types of prizes is 2, with the number of items of type 'a' being 1 and type 'b' being 99.
Answer: (2)
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Question: 2
What is the maximum possible number of different types of prizes?
What is the maximum possible number of different types of prizes?
Updated On: Jul 11, 2024
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Correct Answer: 6
Solution and Explanation
The analysis concludes that the minimum number of boxes for each type follows a pattern of doubling. It is noted that having 7 types of prizes is not possible due to the resulting total number of boxes exceeding 127. However, having 6 types of prizes is feasible, as demonstrated with the example given.
Therefore, the maximum possible number of different types of prizes is 6.
Answer: (6) is correct based on the analysis.
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Question: 3
Which of the following is not possible?
Which of the following is not possible?
Updated On: Aug 20, 2024
- There are exactly 30 items of type b.
- There are exactly 45 items of type c.
- There are exactly 75 items of type e.
- There are exactly 60 items of type d.
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The Correct Option is B
Solution and Explanation
The analysis discusses the possibilities for the number of items for different types and identifies specific constraints. It determines that there cannot be exactly 45 items of type c because it would lead to an inconsistency in the total number of items.Therefore, the statement "There are exactly 45 items of type c" is incorrect based on the given constraints and analysis.
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Question: 4
You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100. What is the maximum possible number of different types of items?
You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100. What is the maximum possible number of different types of items?
Updated On: Aug 20, 2024
- 6
- 3
- 5
- 4
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The Correct Option is C
Solution and Explanation
The analysis concludes that the maximum possible number of different types of items is 5, as the maximum number of items belongs to type e (75 items). It provides a detailed explanation of the reasoning behind this conclusion, considering the constraints on the number of items for each type.
Therefore, the statement "Answer: (5)" accurately summarizes the maximum possible number of different types of items based on the given analysis.
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