100 people took the test of which perfect score is 100.
As a result, the highest score was 90 points ans the lowest score was 20 points.
The average of all people was 75 points.
All the scores are integers.
Among the number of people whose score was less than the average, find the number of people in case the number is least.
Answer
Three people
Solution
The number of people who took 76 points should be most as many as possible.
Answer
Three people
Solution
The number of people who took 76 points should be most as many as possible.
When removing 2 people who took 90 points and 20 points, 100 - 2 = 98 people.
The total score of 98 people is 75 × 100 - (90 + 20) = 7390 points.
7390 - 20 × 98 = 5430
5430/(76-20) = 96.----
Because 7390 - 76 × 96 = 94, sum of 98 - 96 = 2 people will become 94 points.
Because 94 = 20 + 74, remaining 2 people took 20 points and 74 points.
Therefore the number of people below the average mark is 2 people of 20 points and 1 person of 74 points, then 3 people in total.
