Question

Divers in a competition are scored by an international panel of judges. The highest and the lowest scores are dropped. The total of the remaining scores is multiplied by the degree of difficulty of the dive. This product is multiplied by 0.6 to determine the final score. The degree of difficulty of a dive is 4.0. The diver’s final score is 97.2. Judges award half or whole points from 0 to 10. What scores could the judges have given the diver?

1. Step-by-step explanation:
calculating backwards :
97.2 is the final score.
this was multiplied in the final step by 0.6, so we divide by 0.6 :
97.2 / 0.6 = 162
this is the result of a multiplication by 4 (difficulty factor).
so, we divide this by 4 and get
40.5
so, this is the total sum of the scores (without the highest and lowest scores).
there is one problem with the question : we don’t know how many judges there were.
clearly, as the highest possible score of one judge is 10, the score sum of 40.5 tell us that there must have been at least 5 “remaining” judges plus the 2 for highest and lowest scores that were dropped. so, at least 7 judges in total.
normally, there would not be more than 10 judges, so there were between 5 and 8 remaining scores.
if there were 5, then they must have given scores around 8 points (40.5 / 5 ≈ 8).
they could have been e.g.
7.0 8.5 9.0 8.0 8.0
and the dropped scores could have been
6.5 and another 9.0
if there were more judges, then the mean value of the remaining scores was lower.
if there were 10 judges (8 remaining), then we would talk about scores around 5 (40.5 / 8 ≈ 5).
they could have been
4.0 4.5 5.5 6.5 6.0 5.0 5.0 4.0
and the dropped scores could have been
4.0 and 7.0