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After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?
- a)7
- b)8
- c)9
- d)10
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
After grading the examination papers of a class of 18 students, a teac...
Let us say that in the initial arrangement the scores of the nineteen students in ascending order is a1 , a2 , a3 , ..., a19, where a1 is the lowest marks scored by any student.
Since these numbers are in arithmetic progression, a2 = a1 + d, a3 = a1 + 2d ... and so on
where d is the common difference of the arithmetic progression.
Since these numbers are in arithmetic progression, a2 = a1 + d, a3 = a1 + 2d ... and so on
where d is the common difference of the arithmetic progression.
= 19[a1 + 9d]
Average of 19 students = a1 + 9d
= Marks obtained by the student ranked 10th
If the student at the 10th rank belonged to the other class then the average of the students will remain unchanged.
Hence, option 4.
Most Upvoted Answer
After grading the examination papers of a class of 18 students, a teac...
The question states that the scores of the students, when arranged in ascending or descending order, form an arithmetic progression. This means that the difference between consecutive scores is constant. Let's denote this constant difference as 'd'.
Let's assume that the scores of the students are denoted by S1, S2, S3, ..., S18.
Since the number of papers that had been graded was one more than the number of students, there must be a duplicate score. Let's denote this duplicate score as Sx.
Now, let's rearrange the scores in ascending order and find the average.
- The sum of the scores in the initial arrangement can be calculated as:
Sum_initial = S1 + S2 + S3 + ... + S18
- The sum of the scores in the rearranged arrangement can be calculated as:
Sum_rearranged = S1 + S2 + S3 + ... + Sx-1 + Sx+1 + ... + S18 + Sx
Since the average remained the same, we can equate the two sums and solve for Sx:
Sum_initial = Sum_rearranged
S1 + S2 + S3 + ... + S18 = S1 + S2 + S3 + ... + Sx-1 + Sx+1 + ... + S18 + Sx
By canceling out the common terms, we get:
Sx = 0
This means that the duplicate score is 0, which is not possible in the context of the problem.
Therefore, our assumption that there is a duplicate score is incorrect.
Since there is no duplicate score, the number of papers that had been graded is equal to the number of students. Therefore, the rank of the student of the other class in the initial arrangement is 18 + 1 = 19.
However, none of the given options match this answer. So, it seems there might be an error in the question or the options provided.
Let's assume that the scores of the students are denoted by S1, S2, S3, ..., S18.
Since the number of papers that had been graded was one more than the number of students, there must be a duplicate score. Let's denote this duplicate score as Sx.
Now, let's rearrange the scores in ascending order and find the average.
- The sum of the scores in the initial arrangement can be calculated as:
Sum_initial = S1 + S2 + S3 + ... + S18
- The sum of the scores in the rearranged arrangement can be calculated as:
Sum_rearranged = S1 + S2 + S3 + ... + Sx-1 + Sx+1 + ... + S18 + Sx
Since the average remained the same, we can equate the two sums and solve for Sx:
Sum_initial = Sum_rearranged
S1 + S2 + S3 + ... + S18 = S1 + S2 + S3 + ... + Sx-1 + Sx+1 + ... + S18 + Sx
By canceling out the common terms, we get:
Sx = 0
This means that the duplicate score is 0, which is not possible in the context of the problem.
Therefore, our assumption that there is a duplicate score is incorrect.
Since there is no duplicate score, the number of papers that had been graded is equal to the number of students. Therefore, the rank of the student of the other class in the initial arrangement is 18 + 1 = 19.
However, none of the given options match this answer. So, it seems there might be an error in the question or the options provided.
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Community Answer
After grading the examination papers of a class of 18 students, a teac...
If the average remained same even after removal of the marks of student from the other class, it means that the other student at got the average mark. The total number of papers graded where 19. therefore he/she will be at 10th position in ranking. So, answer is option d) 10.
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After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer?
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After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. 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 After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer?.
After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. 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 After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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