SOLUTION: The arithmetic mean of 25 scores on a 100-point test is 87, and the arithmetic mean of 21 of these scores is 85. What is the largest possible difference between any two of the othe

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Question 1035821: The arithmetic mean of 25 scores on a 100-point test is 87, and the arithmetic mean of 21 of these scores is 85. What is the largest possible difference between any two of the other four scores?
Answer by robertb(5830) About Me  (Show Source):
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The 25 scores with a mean of 87 ==> the sum of the 25 scores is 2175.
The 21 of the 25 scores having a mean of 85 ==> the sum of the 21 scores is 1785.
==> Four of the scores had a sum of 2175 - 1785 = 390.
The mean of these four scores is 97.5.
The most a score can vary from 97.5 is 2.5 points. (Assuming that scoring more than 100 is not allowed.)
==> The lowest possible score from the fours scores is 95, while the highest possible is 100.
==> The largest possible difference between any two of the other four scores is 5.