# A CAT aspirant appears for a certain number | Quantitative Aptitude Arithmetic | Averages

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## CAT 2018 - Slot-1 - Arithmetic - Question-5 - A CAT aspirant appears for a certain number

Q. 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

let total number test taken by him = n and average score = x

So average score of last (n-10) test = x+1

Sum of scores of last n-10 test = (n-10)*(x+1) = nx – ( 10x – n + 10)

So total score of first 10 test = 10x – n + 10

20*10 = 10x – n + 10

10x – n = 190  —————1)

average score of first (n-10) test = x-1

Sum of scores of first n-10 test = (n-10)*(x-1) = nx – ( n +10x – 10)

So total score of first 10 test = ( n +10x – 10)

30*10 = ( n +10x – 10)

n + 10x = 310 —————2)

by solving eq 1 ) & eq 2)

n = 60, x = 25

so total number of test taken by him = 60

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