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Exam Averages and Individual Score Calculation

CAT 2019 Slot 1 · Quantitative Ability · Medium · Averages

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Averages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is

  1. A.

    51

  2. B.

    53

  3. C.

    49

  4. D.

    48

Answer

A

Explanation

Let total score of all 22 students be SS. Sum without Gautam =S−G=21×62=1302  ⟹  S=1302+G= S - G = 21 \times 62 = 1302 \implies S = 1302 + G. Average of all 22 students =S22= \frac{S}{22}. Sum without Ramesh =S−82.5= S - 82.5. Average without Ramesh =S−82.521= \frac{S - 82.5}{21}. Given: S22=S−82.521+1\frac{S}{22} = \frac{S - 82.5}{21} + 1. S22−S21=1−82.521=1−3.92857=−2.92857\frac{S}{22} - \frac{S}{21} = 1 - \frac{82.5}{21} = 1 - 3.92857 = -2.92857. −S22×21=21−82.521=−61.521  ⟹  S=22×61.5=1353\frac{-S}{22 \times 21} = \frac{21 - 82.5}{21} = \frac{-61.5}{21} \implies S = 22 \times 61.5 = 1353. G=S−1302=1353−1302=51G = S - 1302 = 1353 - 1302 = 51.

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