Question

In a Mock CAT, 123 students appeared and the average score obtained was 120. But later it was found that the top three students were repeaters, so their score has been eliminated and then the new average score was found to be decreased by 1.5. Also, it is known that all the students obtained the marks in integers and the scores of the toppers were distinct. If the second highest topper has scored more than 185 marks, then the highest possible score of the third highest topper is :

• A. 166
• B. 167
• C. 168
• D. 170

Answer 1

The correct option is B

167

Difference in average = 1.5.
So, total score of 3 toppers = $120\times 3+(123-3)\times 1.5=540.$
Since, second highest topper has scored more than 185 marks and the scores of the toppers were distinct,
So, Score of second topper = 186.
Score of first topper = 187.
$\therefore$ Score of third topper = 540 - (186 + 187) = 167.

Alternatively:
The total score of 3 toppers = 123 $\times$ 120 - 120 $\times$ 118.5 = 540
The highest possible score of the third highest topper is possible when the scores of other two toppers were minimum. So,
$\begin{array}{c}{1}^{st}ranke{r}^{\prime }sscore=187\left(\text{minimum}\right)\\ 2^{nd}ranke{r}^{\prime }sscore=186\left(\text{minimum}\right)\\ 3^{rd}ranke{r}^{\prime }sscore=167\left(\text{maximum}\right)\end{array}\}540$