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16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?
- a)At least two students made the same number of mistakes
- b)Exactly two students made the same number of mistakes
- c)At most two students made the same number of mistakes
- d)All students made different number of mistakes.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
16 students were writing a test in a class. Rahul made 14 mistakes in ...
The number of mistakes made by all the students will be between 0 and 14, i.e., students are having a total of 15 options to make mistakes. Since the number of students = 16, at least two students will have the same number of mistakes (that can be zero also, i.e., two students are making no mistakes). Hence, option 1 is the answer.
Most Upvoted Answer
16 students were writing a test in a class. Rahul made 14 mistakes in ...
Given information:
- 16 students were writing a test in a class.
- Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student.
To determine which of the statements is definitely true, let's consider all the possible scenarios:
- Scenario 1: All students made different numbers of mistakes.
- In this scenario, Rahul made the highest number of mistakes, which is 14. Therefore, there must be 15 different numbers of mistakes made by the other students.
- However, since there are only 15 students left, one of them must have made the same number of mistakes as another student, which means that statement a) is true.
- Scenario 2: At most two students made the same number of mistakes.
- In this scenario, let's assume that two students made the same number of mistakes, and all the other students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than the two students who made the same number of mistakes.
- Therefore, the maximum number of mistakes that the other two students could have made is 13.
- This means that there are only 14 different numbers of mistakes among the 16 students, which contradicts the assumption that at most two students made the same number of mistakes. Therefore, statement c) is false.
- Scenario 3: Exactly two students made the same number of mistakes.
- In this scenario, let's assume that two students made the same number of mistakes, and all the other students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than the two students who made the same number of mistakes.
- Therefore, the maximum number of mistakes that the other two students could have made is 13.
- This means that there are only 14 different numbers of mistakes among the 16 students, which is possible if exactly two students made the same number of mistakes.
- However, we are not given any information to confirm this assumption. Therefore, statement b) cannot be definitely true.
- Scenario 4: At least two students made the same number of mistakes.
- In this scenario, let's assume that all the students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than any other student.
- Therefore, the 15 remaining students must have made 15 different numbers of mistakes, which is not possible since there are only 14 possible numbers of mistakes (from 0 to 13).
- This means that there must be at least two students who made the same number of mistakes, which confirms that statement a) is definitely true.
Therefore, the correct answer is option a) - At least two students made the same number of mistakes.
- 16 students were writing a test in a class.
- Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student.
To determine which of the statements is definitely true, let's consider all the possible scenarios:
- Scenario 1: All students made different numbers of mistakes.
- In this scenario, Rahul made the highest number of mistakes, which is 14. Therefore, there must be 15 different numbers of mistakes made by the other students.
- However, since there are only 15 students left, one of them must have made the same number of mistakes as another student, which means that statement a) is true.
- Scenario 2: At most two students made the same number of mistakes.
- In this scenario, let's assume that two students made the same number of mistakes, and all the other students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than the two students who made the same number of mistakes.
- Therefore, the maximum number of mistakes that the other two students could have made is 13.
- This means that there are only 14 different numbers of mistakes among the 16 students, which contradicts the assumption that at most two students made the same number of mistakes. Therefore, statement c) is false.
- Scenario 3: Exactly two students made the same number of mistakes.
- In this scenario, let's assume that two students made the same number of mistakes, and all the other students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than the two students who made the same number of mistakes.
- Therefore, the maximum number of mistakes that the other two students could have made is 13.
- This means that there are only 14 different numbers of mistakes among the 16 students, which is possible if exactly two students made the same number of mistakes.
- However, we are not given any information to confirm this assumption. Therefore, statement b) cannot be definitely true.
- Scenario 4: At least two students made the same number of mistakes.
- In this scenario, let's assume that all the students made different numbers of mistakes.
- Since Rahul made the highest number of mistakes, he must have made more mistakes than any other student.
- Therefore, the 15 remaining students must have made 15 different numbers of mistakes, which is not possible since there are only 14 possible numbers of mistakes (from 0 to 13).
- This means that there must be at least two students who made the same number of mistakes, which confirms that statement a) is definitely true.
Therefore, the correct answer is option a) - At least two students made the same number of mistakes.
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Community Answer
16 students were writing a test in a class. Rahul made 14 mistakes in ...
Given information:
- 16 students were writing a test.
- Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student.
To determine which statement is definitely true, we need to consider the possible scenarios for the number of mistakes made by the other 15 students.
Scenario 1: All 15 students made fewer than 14 mistakes.
In this scenario, Rahul made the most mistakes and all other students made fewer mistakes than he did. Therefore, each of the 15 students made a different number of mistakes. This scenario satisfies option D.
Scenario 2: One student made exactly 14 mistakes.
In this scenario, Rahul made the most mistakes and one other student made the same number of mistakes as he did. Therefore, at least two students made the same number of mistakes. This scenario satisfies option A and eliminates option D.
Scenario 3: Two or more students made exactly 14 mistakes.
In this scenario, Rahul made the most mistakes and at least two other students made the same number of mistakes as he did. Therefore, at least two students made the same number of mistakes. This scenario satisfies option A and eliminates option C.
Therefore, the only statement that is definitely true is option A: at least two students made the same number of mistakes.
- 16 students were writing a test.
- Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student.
To determine which statement is definitely true, we need to consider the possible scenarios for the number of mistakes made by the other 15 students.
Scenario 1: All 15 students made fewer than 14 mistakes.
In this scenario, Rahul made the most mistakes and all other students made fewer mistakes than he did. Therefore, each of the 15 students made a different number of mistakes. This scenario satisfies option D.
Scenario 2: One student made exactly 14 mistakes.
In this scenario, Rahul made the most mistakes and one other student made the same number of mistakes as he did. Therefore, at least two students made the same number of mistakes. This scenario satisfies option A and eliminates option D.
Scenario 3: Two or more students made exactly 14 mistakes.
In this scenario, Rahul made the most mistakes and at least two other students made the same number of mistakes as he did. Therefore, at least two students made the same number of mistakes. This scenario satisfies option A and eliminates option C.
Therefore, the only statement that is definitely true is option A: at least two students made the same number of mistakes.
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16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer?
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16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer?.
16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer?.
Solutions for 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 16 students were writing a test in a class. Rahul made 14 mistakes in the paper, which was the highest number of mistakes made by any student. Which of the following statements is definitely true?a)At least two students made the same number of mistakesb)Exactly two students made the same number of mistakesc)At most two students made the same number of mistakesd)All students made different number of mistakes.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.
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