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CAT 2019 Slot 1 — QA Question 17

Change in AverageEasy

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

Answer & solution

  • A

    53

  • 51

  • C

    49

  • D

    48

Solution

Easy

Let TT be the total of all 22 scores and GG Gautam's score. Write TT two ways — excluding Gautam (avg 62) and excluding Ramesh (avg xx, score 82.5) — then use the relation "overall average is 1 more than the average without Ramesh" to solve.

1

Total via "without Gautam". The other 21 average 62.

G+62×21=T⇒ T=G+1302(I)\begin{aligned} &G+62\times21=T\\ &\Rightarrow\ T=G+1302 \quad\text{(I)} \end{aligned}
2

Total via "without Ramesh". Let those 21 average xx; Ramesh scored 82.5.

82.5+21x=T(II)\begin{aligned} &82.5+21x=T \quad\text{(II)} \end{aligned}
3

Average condition. Overall average is 1 more than xx.

T22=x+1⇒ T=22x+22(III)\begin{aligned} &\frac{T}{22}=x+1\\ &\Rightarrow\ T=22x+22 \quad\text{(III)} \end{aligned}
4

Solve. Equate (II) and (III) for xx, then back-substitute.

82.5+21x=22x+22[(II)=(III)]⇒ x=60.5⇒ T=22(60.5)+22=1353(III)⇒ G=T−1302=1353−1302=51(I)\begin{aligned} &82.5+21x=22x+22\quad\text{[(II)=(III)]}\\ &\Rightarrow\ x=60.5\\ &\Rightarrow\ T=22(60.5)+22=1353\quad\text{(III)}\\ &\Rightarrow\ G=T-1302=1353-1302=51\quad\text{(I)} \end{aligned}
Gautam’s score=51\text{Gautam's score}=51
CAT 2019 Slot 1 QA Q17: Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the — Solution | TheCATExam