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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?
What is the highest possible value of the average of these 20 integers?
- a)3.5
- b)5
- c)4.5
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The average of 30 integers is 5. Among these 30 integers, there are ex...
It is given that the average of the 30 integers = 5
Sum of the 30 integers = 30*5=150
There are exactly 20 integers whose value is less than 5.
To maximise the average of the 20 integers, we have to assign minimum value to each of the remaining 10 integers
So the sum of 10 integers = 10*6=60
The sum of the 20 integers = 150-60= 90
Average of 20 integers = 90 / 20 = 4.5
Sum of the 30 integers = 30*5=150
There are exactly 20 integers whose value is less than 5.
To maximise the average of the 20 integers, we have to assign minimum value to each of the remaining 10 integers
So the sum of 10 integers = 10*6=60
The sum of the 20 integers = 150-60= 90
Average of 20 integers = 90 / 20 = 4.5
Most Upvoted Answer
The average of 30 integers is 5. Among these 30 integers, there are ex...
To find the highest possible value of the average of the 20 integers, we need to consider the range of numbers that fall within the given conditions.
Given that the average of 30 integers is 5, we can calculate the sum of all the integers as follows:
Average = Sum of Integers / Number of Integers
5 = Sum of Integers / 30
Sum of Integers = 5 * 30 = 150
Since there are exactly 20 integers that do not exceed 5, we can assume that the remaining 10 integers exceed 5. Let's denote the sum of the 20 integers that do not exceed 5 as 'x'. Therefore, the sum of the remaining 10 integers would be 150 - x.
Now, we can find the average of the 20 integers that do not exceed 5:
Average = Sum of Integers / Number of Integers
x / 20 = 5
x = 100
So, the highest possible value of the average of these 20 integers is 100 / 20 = 5.
Therefore, the correct answer is option C) 4.5.
Given that the average of 30 integers is 5, we can calculate the sum of all the integers as follows:
Average = Sum of Integers / Number of Integers
5 = Sum of Integers / 30
Sum of Integers = 5 * 30 = 150
Since there are exactly 20 integers that do not exceed 5, we can assume that the remaining 10 integers exceed 5. Let's denote the sum of the 20 integers that do not exceed 5 as 'x'. Therefore, the sum of the remaining 10 integers would be 150 - x.
Now, we can find the average of the 20 integers that do not exceed 5:
Average = Sum of Integers / Number of Integers
x / 20 = 5
x = 100
So, the highest possible value of the average of these 20 integers is 100 / 20 = 5.
Therefore, the correct answer is option C) 4.5.
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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?a)3.5b)5c)4.5d)4Correct answer is option 'C'. Can you explain this answer?
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