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Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. X is the maximum number of boxes containing the same number of oranges. What is the minimum value of X?
- a)5
- b)103
- c)6
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Of 128 boxes of oranges, each box contains at least 120 and at most 14...
Understanding the Problem
We have 128 boxes of oranges, with each box containing between 120 and 144 oranges. We want to find the minimum number of boxes, X, that can contain the same number of oranges.
Possible Orange Counts
- The range of oranges per box is from 120 to 144.
- This gives us a total of 25 different possible counts:
- 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144.
Using the Pigeonhole Principle
- According to the Pigeonhole Principle, if you have more items (boxes) than containers (possible orange counts), at least one container must hold more than one item.
- In this case, we have 128 boxes (items) and 25 possible counts (containers).
Calculating Minimum Value of X
- To find the minimum value of X, we can divide the total number of boxes by the number of different counts:
128 boxes ÷ 25 counts = 5.12
- Since X must be a whole number, we round up to 6. This means at least one count must have at least 6 boxes.
Conclusion
- Thus, the minimum value of X, which represents the maximum number of boxes containing the same number of oranges, is 6.
Therefore, the correct answer is option 'C'.
We have 128 boxes of oranges, with each box containing between 120 and 144 oranges. We want to find the minimum number of boxes, X, that can contain the same number of oranges.
Possible Orange Counts
- The range of oranges per box is from 120 to 144.
- This gives us a total of 25 different possible counts:
- 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144.
Using the Pigeonhole Principle
- According to the Pigeonhole Principle, if you have more items (boxes) than containers (possible orange counts), at least one container must hold more than one item.
- In this case, we have 128 boxes (items) and 25 possible counts (containers).
Calculating Minimum Value of X
- To find the minimum value of X, we can divide the total number of boxes by the number of different counts:
128 boxes ÷ 25 counts = 5.12
- Since X must be a whole number, we round up to 6. This means at least one count must have at least 6 boxes.
Conclusion
- Thus, the minimum value of X, which represents the maximum number of boxes containing the same number of oranges, is 6.
Therefore, the correct answer is option 'C'.
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Community Answer
Of 128 boxes of oranges, each box contains at least 120 and at most 14...
Each box contains at least 120 and at most 144 oranges.
So boxes may contain 25 different numbers of oranges among 120, 121, 122, .... 144.
Lets start counting. 1st 25 boxes contain different numbers of oranges and this is repeated till 5 sets as 25*5=125.
Now we have accounted for 125 boxes. Still 3 boxes are remaining. These 3 boxes can have any number of oranges from 120 to 144.
Already every number is in 5 boxes. Even if these 3 boxes have different number of oranges, some number of oranges will be in 6 boxes.
Hence the number of boxes containing the same number of oranges is at least 6.
So boxes may contain 25 different numbers of oranges among 120, 121, 122, .... 144.
Lets start counting. 1st 25 boxes contain different numbers of oranges and this is repeated till 5 sets as 25*5=125.
Now we have accounted for 125 boxes. Still 3 boxes are remaining. These 3 boxes can have any number of oranges from 120 to 144.
Already every number is in 5 boxes. Even if these 3 boxes have different number of oranges, some number of oranges will be in 6 boxes.
Hence the number of boxes containing the same number of oranges is at least 6.
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Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. X is the maximum number of boxes containing the same number of oranges. What is the minimum value of X?a)5b)103c)6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. X is the maximum number of boxes containing the same number of oranges. What is the minimum value of X?a)5b)103c)6d)Cannot be determinedCorrect 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 Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. X is the maximum number of boxes containing the same number of oranges. What is the minimum value of X?a)5b)103c)6d)Cannot be determinedCorrect 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 Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. X is the maximum number of boxes containing the same number of oranges. What is the minimum value of X?a)5b)103c)6d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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