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Directions for Questions: 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.
(2019)
Q. 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?
  • a)
    6
  • b)
    3
  • c)
    5
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Directions for Questions: A new game show on TV has 100 boxes numbered...
The maximum possible number of prizes can be 5. In that case, the maximum possible number of items should belong to type e. There can 75 items of type e, when the number of items of type b, c and d are 2, 4 and 18 respectively.
Therefore, the maximum possible number of different type of items is 5.
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Most Upvoted Answer
Directions for Questions: A new game show on TV has 100 boxes numbered...
The maximum possible number of prizes can be 5. In that case, the maximum possible number of items should belong to type e. There can 75 items of type e, when the number of items of type b, c and d are 2, 4 and 18 respectively.
Therefore, the maximum possible number of different type of items is 5.
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Community Answer
Directions for Questions: A new game show on TV has 100 boxes numbered...
Explanation:

Given Information:
- There are 31 items of the same type as box 45 in boxes 1 to 44.
- There are 43 items of the same type as box 45 in boxes 46 to 100.

Analysis:
- Since the number of items at least doubles as you move to the next type, we can deduce that the number of items of the same type as box 45 in the boxes before and after box 45 are related.
- The number of items of the same type as box 45 in the boxes before box 45 should be half the number of items in the boxes after box 45.

Solution:
- Let's assume there are 'n' types of items.
- From the given information, we know that the number of items of the same type as box 45 in boxes 1 to 44 is 31, and in boxes 46 to 100 is 43.
- Therefore, the total number of items of the same type as box 45 in all boxes should be 31 + 1 + 43 = 75.
- Since the number of items of the same type as box 45 in the boxes before and after box 45 are related, the number of items in each half should be 37.5.
- This means that there cannot be half items, so we need to consider the next whole number, which is 38.
- Therefore, the maximum possible number of different types of items is 5 (a, b, c, d, e).
Thus, the correct answer is option C - 5.
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Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer?
Question Description
Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct 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 Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct 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 Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer?.
Solutions for Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
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Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Directions for Questions: 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 isexactly 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.(2019)Q. 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?a)6b)3c)5d)4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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