Abhishek was playing an interesting timed game in which he was supposed to pick up the marbles scattered on the floor in exactly 5 minutes from the time the buzzer went off. During each of his 25 attempts, he tried to pick up the maximum number of marbles lying on the floor. However, after a certain number of attempts, he forgot the count of marbles he had picked up in each of the previous rounds. The only figure he could remember now was that he had picked up a total of 337 marbles in the first 5 rounds. Further, he never picked up the same number of marbles in any of the rounds and always picked a number of marbles less than the number of marbles picked up by him in the previous round.Q. If Abhishek had picked up 121 marbles in the last five rounds then the average number of marbles he could have picked up in all rounds put together can be at most: (Round off any fraction to the next higher integer.)Correct answer is '53'. Can you explain this answer?

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Abhishek was playing an interesting timed game in which he was supposed to pick up the marbles scattered on the floor in exactly 5 minutes from the time the buzzer went off. During each of his 25 attempts, he tried to pick up the maximum number of marbles lying on the floor. However, after a certain number of attempts, he forgot the count of marbles he had picked up in each of the previous rounds. The only figure he could remember now was that he had picked up a total of 337 marbles in the first 5 rounds. Further, he never picked up the same number of marbles in any of the rounds and always picked a number of marbles less than the number of marbles picked up by him in the previous round.

Q. If Abhishek had picked up 121 marbles in the last five rounds then the average number of marbles he could have picked up in all rounds put together can be at most: (Round off any fraction to the next higher integer.)

Correct answer is '53'. Can you explain this answer?

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Abhishek was playing an interesting timed game in which he was suppose...

In first five rounds he had picked up 337 marbles while in last five rounds he had picked up 121 marbles, the average number of marbles picked up by him will be highest when he picks up the maximum number of marbles from round 6th to round 20th.
To maximize the number of marbles picked up by him in 6th round, let us distribute the number of marbles in first five rounds as equally as possible.
The possible distribution can be 70, 69, 67, 66 and 65 OR 71,68, 67, 66 and 65.
The maximum number of marbles he could have picked up in round 6 can be 64.
To maximize the average, let the number of marbles picked by him be as shown in the table.

The total number of marbles picked by him will be 337 + 121 + 855 = 1313
The average would be 1313/25 = 52.52 Rounding off to the next higher integer the required answer would be 53.
Answer: 53

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Abhishek was playing an interesting timed game in which he was suppose...

Calculating the Maximum Average Number of Marbles:
To find the maximum average number of marbles Abhishek could have picked up in all rounds put together, we first need to calculate the total number of marbles he picked up in the last five rounds. Given that he picked up 121 marbles in the last five rounds, we can deduce the following:
- Abhishek picked up a total of 337 marbles in the first 5 rounds.
- Therefore, he must have picked up 337 - 121 = 216 marbles in the first 20 rounds (25 rounds total - last 5 rounds).
- Now, we know that he never picked up the same number of marbles in any round and always picked up fewer marbles than in the previous round.

Finding the Maximum Average:
To maximize the average number of marbles, Abhishek would have picked up in all rounds put together, he would have picked up the maximum number of marbles in each of the first 20 rounds. We can distribute the 216 marbles over these 20 rounds in such a way that each subsequent round has fewer marbles than the previous round.
- The sum of the first 20 natural numbers is 20 * (20 + 1) / 2 = 210.
- Therefore, the maximum average number of marbles Abhishek could have picked up in all rounds put together would be 210 / 20 = 10.
- Adding the 121 marbles from the last five rounds, the total number of marbles picked up would be 210 + 121 = 331.
- To find the average, we divide the total by the number of rounds: 331 / 25 = 13.24, rounded up to 14.
Therefore, the maximum average number of marbles Abhishek could have picked up in all rounds put together is 14 (rounded up from 13.24).

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Abhishek was playing an interesting timed game in which he was supposed to pick up the marbles scattered on the floor in exactly 5 minutes from the time the buzzer went off. During each of his 25 attempts, he tried to pick up the maximum number of marbles lying on the floor. However, after a certain number of attempts, he forgot the count of marbles he had picked up in each of the previous rounds. The only figure he could remember now was that he had picked up a total of 337 marbles in the first 5 rounds. Further, he never picked up the same number of marbles in any of the rounds and always picked a number of marbles less than the number of marbles picked up by him in the previous round.Q. If Abhishek had picked up 121 marbles in the last five rounds then the average number of marbles he could have picked up in all rounds put together can be at most: (Round off any fraction to the next higher integer.)Correct answer is '53'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Abhishek was playing an interesting timed game in which he was supposed to pick up the marbles scattered on the floor in exactly 5 minutes from the time the buzzer went off. During each of his 25 attempts, he tried to pick up the maximum number of marbles lying on the floor. However, after a certain number of attempts, he forgot the count of marbles he had picked up in each of the previous rounds. The only figure he could remember now was that he had picked up a total of 337 marbles in the first 5 rounds. Further, he never picked up the same number of marbles in any of the rounds and always picked a number of marbles less than the number of marbles picked up by him in the previous round.Q. If Abhishek had picked up 121 marbles in the last five rounds then the average number of marbles he could have picked up in all rounds put together can be at most: (Round off any fraction to the next higher integer.)Correct answer is '53'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Abhishek was playing an interesting timed game in which he was supposed to pick up the marbles scattered on the floor in exactly 5 minutes from the time the buzzer went off. During each of his 25 attempts, he tried to pick up the maximum number of marbles lying on the floor. However, after a certain number of attempts, he forgot the count of marbles he had picked up in each of the previous rounds. The only figure he could remember now was that he had picked up a total of 337 marbles in the first 5 rounds. Further, he never picked up the same number of marbles in any of the rounds and always picked a number of marbles less than the number of marbles picked up by him in the previous round.Q. If Abhishek had picked up 121 marbles in the last five rounds then the average number of marbles he could have picked up in all rounds put together can be at most: (Round off any fraction to the next higher integer.)Correct answer is '53'. Can you explain this answer?.

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