CAT 2018 Question Paper | Quants Slot 1

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Question 5 :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 [TITA]

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Averages

Let there be 'n' tests and the Overall Average score be k
Average (n) = k => Total marks = nk
So, when we ignore the first 10 questions,
Average (n-10) = k+1
Similarly, if we ignore the last 10 questions,
Average (first (n-10)) = k-1

It is given that when the first 10 tests are not considered, the overall average increases by 1 (Each question carries 20 marks)
Total marks – 20×10 = (k+1) (n-10)
kn – 200 = (k+1) (n-10) ---(1)
Similarly, If the last 10 tests are not considered, the overall average decreases by 1 (Each question carries 30 marks)
kn - 300 = (k-1) (n-10) ---(2)

Solving (1) and (2), we get
kn - 200 = (k+1) (n-10)
(-) kn - 300 = (k-1) (n-10)
-------------------------------------
100 = 2(n-10)
50 = n-10
n = 60 questions

The question is "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 [TITA]"

Hence, the answer is 60 questions