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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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Verified Answer
A CAT aspirant appears for a certain number of tests. His average sco...
Let the total number of tests be 'n' and the average by 'A'
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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 sco...
Total Number of Tests Calculation
To solve the problem, let's define some variables:
- Let \( n \) = total number of tests taken
- Let \( S \) = total score of all tests
Given:
- Average score increases by 1 when the first 10 tests are excluded.
- Average score decreases by 1 when the last 10 tests are excluded.
- Average score of the first 10 tests = 20, hence total score of first 10 tests \( = 20 \times 10 = 200 \).
- Average score of the last 10 tests = 30, hence total score of last 10 tests \( = 30 \times 10 = 300 \).
Now, calculate the average scores:
When First 10 Tests are Excluded
- New total score excluding the first 10 tests:
\[
S - 200
\]
- Number of tests left:
\[
n - 10
\]
- New average after excluding the first 10 tests:
\[
\frac{S - 200}{n - 10} = \frac{S}{n} + 1
\]
When Last 10 Tests are Excluded
- New total score excluding the last 10 tests:
\[
S - 300
\]
- Number of tests left:
\[
n - 10
\]
- New average after excluding the last 10 tests:
\[
\frac{S - 300}{n - 10} = \frac{S}{n} - 1
\]
Setting Up the Equations
From the first condition:
\[
S - 200 = \left(\frac{S}{n} + 1\right)(n - 10)
\]
From the second condition:
\[
S - 300 = \left(\frac{S}{n} - 1\right)(n - 10)
\]
Solving the Equations
1. Expand both equations and simplify.
2. From simplifications, you will derive \( n = 60 \).
Thus, the total number of tests taken by him is **60**.
To solve the problem, let's define some variables:
- Let \( n \) = total number of tests taken
- Let \( S \) = total score of all tests
Given:
- Average score increases by 1 when the first 10 tests are excluded.
- Average score decreases by 1 when the last 10 tests are excluded.
- Average score of the first 10 tests = 20, hence total score of first 10 tests \( = 20 \times 10 = 200 \).
- Average score of the last 10 tests = 30, hence total score of last 10 tests \( = 30 \times 10 = 300 \).
Now, calculate the average scores:
When First 10 Tests are Excluded
- New total score excluding the first 10 tests:
\[
S - 200
\]
- Number of tests left:
\[
n - 10
\]
- New average after excluding the first 10 tests:
\[
\frac{S - 200}{n - 10} = \frac{S}{n} + 1
\]
When Last 10 Tests are Excluded
- New total score excluding the last 10 tests:
\[
S - 300
\]
- Number of tests left:
\[
n - 10
\]
- New average after excluding the last 10 tests:
\[
\frac{S - 300}{n - 10} = \frac{S}{n} - 1
\]
Setting Up the Equations
From the first condition:
\[
S - 200 = \left(\frac{S}{n} + 1\right)(n - 10)
\]
From the second condition:
\[
S - 300 = \left(\frac{S}{n} - 1\right)(n - 10)
\]
Solving the Equations
1. Expand both equations and simplify.
2. From simplifications, you will derive \( n = 60 \).
Thus, the total number of tests taken by him 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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