Ten friends went to a play arena to play archery. Each of them was

Solution

Given:
• Ten friends are playing archery.
• One can get only one of the six scores: 20, 40, 60, 80 and 100 or 0.
• At the end of the game, three friends scored 0, one friend 20, two friends 40, one friend 100 and the sum of the scores of remaining three is equal to 240

To find:
• The median score of all the three friends.

Approach and Working:

• We can arrange the score of seven friends as: 0, 0, 0 ,20, 40, 40,100

• We still need to find the score of remaining three friends to find the median score.
o Let us assume they scored a, b, and c.
o a + b + c =240
o As maximum score can be 240 only, hence their score can be:
 80,80,80

• In this case, the median will be 40.
 Or 100,100,40

• In this case, the median will be 40.
 Or 100, 80, 60

• In this case, the median will be 40.

In all the cases, the median is 40.
Hence, the correct answer is option C.

Answer: C

Hi , I was just thinking , do we need to know the some of the rest 3 players ?
I mean from the language of the question , when we say for example , 3 scored zero , doesn't that mean that no other players scored zeros ?
Thanks

I chose a little different approach:

So we know, that in order to find the median, we need to find the mean of the 5th and 6th number (sorted in ascending order):
0 - 0 - 0 - 20 - 40 - 40 - _ - _ - _ - 100

Currently, the median 'would' be 40 (40+40/2).
If we would add numbers on the right side (40, 60, 80, 100), the median wouldn't change as the 5th and 6th number will be the same.
Therefore, we need to check if it is possible to insert numbers on the left side.

So we check if it's possible to create 240 where at least one value is 0, 20 or 40:
0: 0 + 100 (highest possible) --> 140 would be needed, so not possible
20: 20 + 100 --> 120 would be needed, so not possible
40: 40 + 100 --> 100 would be needed. Possible, but it wouldn't change the median.

Therefor we can say that 40 is the median, regardless of the missing scores.