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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is
Correct answer is '60'. Can you explain this answer?
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A CAT aspirant appears for a certain number of tests. His average scor...
Let the total number of tests be 'n' and the average by 'A'
Total score = n*A
When 1st 10 tests are excluded, decrease in total value of scores = (nA - 20 * 10) = (nA - 200)
Also, (n - 10)(A + 1) = (nA - 200)
On solving, we get 10A - n = 190..........(i)
When last 10 tests are excluded, decrease in total value of scores = (nA - 30 * 10) = (nA - 300)
Also, (n - 10)(A - 1) = (nA - 300)
On solving, we get 10A + n = 310..........(ii) From (i) and (ii), we get n = 60
Hence, 60 is the correct answer.
Total score = n*A
When 1st 10 tests are excluded, decrease in total value of scores = (nA - 20 * 10) = (nA - 200)
Also, (n - 10)(A + 1) = (nA - 200)
On solving, we get 10A - n = 190..........(i)
When last 10 tests are excluded, decrease in total value of scores = (nA - 30 * 10) = (nA - 300)
Also, (n - 10)(A - 1) = (nA - 300)
On solving, we get 10A + n = 310..........(ii) From (i) and (ii), we get n = 60
Hence, 60 is the correct answer.
Most Upvoted Answer
A CAT aspirant appears for a certain number of tests. His average scor...
Solution:
Let the total number of tests taken by the CAT aspirant be 'n'.
Given, his average score increases by 1 if the first 10 tests are not considered.
So, the average score of remaining (n-10) tests = previous average + 1
Similarly, the average score decreases by 1 if the last 10 tests are not considered.
So, the average score of remaining (n-10) tests = previous average - 1
Now, we have to find the value of 'n'.
Given, the average score for the first 10 tests = 20
So, the total score of first 10 tests = 20*10 = 200
Given, the average score for the last 10 tests = 30
So, the total score of last 10 tests = 30*10 = 300
Let the total score of remaining (n-20) tests be 'x'.
So, the total score of all n tests = 200 + x + 300 = x + 500
Also, we know that the average score of remaining (n-10) tests = previous average + 1
=> x/(n-10) = (20+1) = 21
=> x = 21(n-10)
Similarly, the average score of remaining (n-10) tests = previous average - 1
=> x/(n-10) = (30-1) = 29
=> x = 29(n-10)
Equating both the expressions of x, we get:
21(n-10) = 29(n-10)
=> 8n = 80
=> n = 10
Therefore, the total number of tests taken by the CAT aspirant is 60.
Let the total number of tests taken by the CAT aspirant be 'n'.
Given, his average score increases by 1 if the first 10 tests are not considered.
So, the average score of remaining (n-10) tests = previous average + 1
Similarly, the average score decreases by 1 if the last 10 tests are not considered.
So, the average score of remaining (n-10) tests = previous average - 1
Now, we have to find the value of 'n'.
Given, the average score for the first 10 tests = 20
So, the total score of first 10 tests = 20*10 = 200
Given, the average score for the last 10 tests = 30
So, the total score of last 10 tests = 30*10 = 300
Let the total score of remaining (n-20) tests be 'x'.
So, the total score of all n tests = 200 + x + 300 = x + 500
Also, we know that the average score of remaining (n-10) tests = previous average + 1
=> x/(n-10) = (20+1) = 21
=> x = 21(n-10)
Similarly, the average score of remaining (n-10) tests = previous average - 1
=> x/(n-10) = (30-1) = 29
=> x = 29(n-10)
Equating both the expressions of x, we get:
21(n-10) = 29(n-10)
=> 8n = 80
=> n = 10
Therefore, the total number of tests taken by the CAT aspirant is 60.
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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer?
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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. 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 A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer?.
A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. 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 A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer?.
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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer?, a detailed solution for A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer? has been provided alongside types of A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him isCorrect answer is '60'. Can you explain this answer? theory, EduRev gives you an
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