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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
(2018)
  • a)
    65
  • b)
    60
  • c)
    50
  • d)
    55
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A CAT aspirant appears for a certain number of tests. His average scor...
Let the average score of the aspirant in all the tests be A. Let the number of tests be N.
The aspirant’s average score for the first 10 tests and last 10 tests are 20 and 30 respectively.

⇒    10A – N = 190 and N + 10A = 310
On subtracting,
we get,  – 2N = – 120
⇒ N = 60.
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Most Upvoted Answer
A CAT aspirant appears for a certain number of tests. His average scor...

Explanation:

Given data:
- Average score of first 10 tests = 20
- Average score of last 10 tests = 30

Approach:
- Let the total number of tests taken be x.
- The total sum of scores for the first 10 tests = 20 * 10 = 200
- The total sum of scores for the last 10 tests = 30 * 10 = 300
- The total sum of scores for all x tests = Average score * x

Solution:
- If the average score increases by 1 when the first 10 tests are not considered, the new average score for the remaining (x-10) tests = 21
- If the average score decreases by 1 when the last 10 tests are not considered, the new average score for the remaining (x-10) tests = 29

- Using the total sum of scores:
- 200 + sum of scores for remaining (x-10) tests = 21 * (x-10)
- 300 + sum of scores for remaining (x-10) tests = 29 * (x-10)

- Solving these equations, we get:
- Sum of scores for remaining (x-10) tests = 210
- Sum of scores for remaining (x-10) tests = 290

- Therefore, x-10 = 10
- x = 20

Conclusion:
- The total number of tests taken by the CAT aspirant is 20. Hence, the correct answer is option B) 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 is(2018)a)65b)60c)50d)55Correct answer is option 'B'. Can you explain this answer?
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