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In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and the average of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?
- a)0
- b)2
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a mid term examination, there are 7 subjects. The maximum marks and...
Ravi's total marks = 40% of 700 = 280
Total score in 3 subjects = 48 x 3 = 144
Since the maximum marks in one of the three given subjects is 64, total marks in the remaining two subjects of this group = 144 - 64 = 80
and, total score in remaining 4 subjects = 136
To find M .
80 can be split as 34 + 46
He can fail in at most one of the three given subjects.
For the remaining 4 subjects, 136 can be split as 34 x 4 i.e. he fails in all four subjects.
M = 4 + 1 = 5
To find m. 80 can be split as 40 + 40.
He doesn't fail in at any of the three given subjects.
For the remaining 4 subjects, 136 can be split as (35 * 3) + 31 i.e. he fails in at most one subject.
m = 1
M-m = 5 - 1 = 4
Hence, option 4.
Total score in 3 subjects = 48 x 3 = 144
Since the maximum marks in one of the three given subjects is 64, total marks in the remaining two subjects of this group = 144 - 64 = 80
and, total score in remaining 4 subjects = 136
To find M .
80 can be split as 34 + 46
He can fail in at most one of the three given subjects.
For the remaining 4 subjects, 136 can be split as 34 x 4 i.e. he fails in all four subjects.
M = 4 + 1 = 5
To find m. 80 can be split as 40 + 40.
He doesn't fail in at any of the three given subjects.
For the remaining 4 subjects, 136 can be split as (35 * 3) + 31 i.e. he fails in at most one subject.
m = 1
M-m = 5 - 1 = 4
Hence, option 4.
Most Upvoted Answer
In a mid term examination, there are 7 subjects. The maximum marks and...
Given information:
- 7 subjects
- Maximum marks and passing marks for each subject are 100 and 35 respectively
- Ravi scored 40% marks in all subjects
- Average of his marks in Mathematics, English and Physics is 48
- Highest marks among these three subjects is 64
- M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed
- Need to find (M-m)
Approach:
- Find Ravi's total marks and compare with passing marks to find number of subjects he failed
- Use the given information about the average marks and highest marks to find which subjects Ravi could have failed
- Calculate M and m based on the above analysis
- Find (M-m)
Detailed solution:
- Ravi scored 40% marks in all subjects, which means he scored (40/100)*7*100 = 280 marks out of 700
- To pass, he needs to score at least 35*7 = 245 marks out of 700
- Therefore, he failed in (700-280)/100 = 4.2 ≈ 4 subjects
- Now, we need to find which subjects he could have failed based on the given information
- Let's assume he scored the highest marks in Mathematics, English and Physics and see if it is possible for him to score an average of 48 in these subjects
- If he scored 64 in each of these subjects and 35 in the remaining 4 subjects, then his total marks would be (64*3 + 35*4) = 271, which is more than the passing marks of 245
- Therefore, it is possible for him to score an average of 48 in Mathematics, English and Physics
- This means he did not fail in any of these subjects
- However, he could have failed in any of the remaining 4 subjects, so m = 0 and M = 4
- Therefore, (M-m) = 4-0 = 4
Answer: Option (d) 4
- 7 subjects
- Maximum marks and passing marks for each subject are 100 and 35 respectively
- Ravi scored 40% marks in all subjects
- Average of his marks in Mathematics, English and Physics is 48
- Highest marks among these three subjects is 64
- M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed
- Need to find (M-m)
Approach:
- Find Ravi's total marks and compare with passing marks to find number of subjects he failed
- Use the given information about the average marks and highest marks to find which subjects Ravi could have failed
- Calculate M and m based on the above analysis
- Find (M-m)
Detailed solution:
- Ravi scored 40% marks in all subjects, which means he scored (40/100)*7*100 = 280 marks out of 700
- To pass, he needs to score at least 35*7 = 245 marks out of 700
- Therefore, he failed in (700-280)/100 = 4.2 ≈ 4 subjects
- Now, we need to find which subjects he could have failed based on the given information
- Let's assume he scored the highest marks in Mathematics, English and Physics and see if it is possible for him to score an average of 48 in these subjects
- If he scored 64 in each of these subjects and 35 in the remaining 4 subjects, then his total marks would be (64*3 + 35*4) = 271, which is more than the passing marks of 245
- Therefore, it is possible for him to score an average of 48 in Mathematics, English and Physics
- This means he did not fail in any of these subjects
- However, he could have failed in any of the remaining 4 subjects, so m = 0 and M = 4
- Therefore, (M-m) = 4-0 = 4
Answer: Option (d) 4
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In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?
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In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct 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 In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct 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 In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?.
In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct 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 In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct 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 In a mid term examination, there are 7 subjects. The maximum marks and passing marks for each subject are 100 and 35 respectively. Ravi scored 40% marks in all and theaverage of his marks in Mathematics, English and Physics is 48, with the highest marks among these three subjects being 64. If M and m are respectively the maximum and minimum number of subjects in which Ravi could have failed, what is (M - m)?a)0b)2c)3d)4Correct answer is option 'D'. Can you explain this answer?.
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