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CAT 2018 [SLOT 1] Quant Question with Solution 20

Question:
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

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Correct Answer: 60
Let the average score of the aspirant in all the tests be x. 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.
$\frac{nx-200}{n-10}=x+1$ and $\frac{nx-300}{n-10}=x-1$
Solving, we get n=60

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