CAT 2020 Slot 2 QA Question 12: In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possib

Question

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possib

Accepted Answer

Let the scores in increasing order be $a_1, a_2, ..., a_{10}$.

$a_1 + a_2 + ... + a_9 = 9 	imes 42 = 378$
$a_2 + a_3 + ... + a_{10} = 9 	imes 47 = 423$

Subtracting the first equation from the second,
$a_{10} - a_1 = 45$

The total sum is
$378 + a_{10} = 423 + a_1$
So the overall mean varies with

In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by