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Question 2 : The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?
We are told that exactly 20 of the 30 integers do not exceed 5...
That means exactly 10 of the 30 integers do exceed 5.
In order to keep the average of the 20 integers as high as possible, we need to keep the average of the 10 integers above 5 as low as possible. Since we are dealing with integers, the least value that the 10 integers above 5 can take is 6.
So, the sum of the 10 integers = 10 * 6 = 60
So the sum of the remainng 20 integers = Total sum - 60 = 5 * 50 - 60 = 90
Hence the average of the remaining 20 is 90/20 = 4.5
The question is "The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?"
Choice C is the correct answer.
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