Some tennis balls are to be put into 7 boxes such that each box contains at least one ball. At the most, 3 of the boxes are to contain the same number of balls, and no two of the remaining boxes are to contain an equal number of balls. What is the least possible number of tennis balls needed for the boxes?a)7b)13c)17d)19Correct answer is option 'C'. Can you explain this answer?

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Some tennis balls are to be put into 7 boxes such that each box contains at least one ball. At the most, 3 of the boxes are to contain the same number of balls, and no two of the remaining boxes are to contain an equal number of balls. What is the least possible number of tennis balls needed for the boxes?

a)
7
b)
13
c)
17
d)
19

Correct answer is option 'C'. Can you explain this answer?

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Some tennis balls are to be put into 7 boxes such that each box contai...

To solve this problem, we need to find the least possible number of tennis balls needed for the boxes while satisfying the given conditions.

Let's analyze the conditions given:

1. Each box should contain at least one ball.
2. At most, 3 of the boxes can contain the same number of balls.
3. No two of the remaining boxes should contain an equal number of balls.

Now, let's consider the possible scenarios:

1. If all 7 boxes contain exactly 1 ball each, we would need a total of 7 balls. However, in this scenario, all the boxes would contain the same number of balls, which violates condition 2.

2. If 1 box contains 1 ball and the remaining 6 boxes contain 2 balls each, we would need a total of 13 balls (1 + 6 * 2 = 13). In this scenario, only 1 box contains a different number of balls, satisfying condition 2. However, there are two boxes with the same number of balls (6 boxes with 2 balls each), violating condition 3.

3. If 1 box contains 1 ball, 3 boxes contain 2 balls each, and the remaining 3 boxes contain 3 balls each, we would need a total of 1 + 3 * 2 + 3 * 3 = 17 balls. In this scenario, only 1 box contains a different number of balls (1 box with 1 ball), satisfying condition 2. Additionally, no two boxes have the same number of balls, satisfying condition 3.

Therefore, the least possible number of tennis balls needed for the boxes is 17 (option C).

Answered by Wizius Careers · View profile

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Some tennis balls are to be put into 7 boxes such that each box contains at least one ball. At the most, 3 of the boxes are to contain the same number of balls, and no two of the remaining boxes are to contain an equal number of balls. What is the least possible number of tennis balls needed for the boxes?a)7b)13c)17d)19Correct 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 Some tennis balls are to be put into 7 boxes such that each box contains at least one ball. At the most, 3 of the boxes are to contain the same number of balls, and no two of the remaining boxes are to contain an equal number of balls. What is the least possible number of tennis balls needed for the boxes?a)7b)13c)17d)19Correct 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 Some tennis balls are to be put into 7 boxes such that each box contains at least one ball. At the most, 3 of the boxes are to contain the same number of balls, and no two of the remaining boxes are to contain an equal number of balls. What is the least possible number of tennis balls needed for the boxes?a)7b)13c)17d)19Correct answer is option 'C'. Can you explain this answer?.

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