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If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
- a)50
- b)52
- c)49
- d)48
- e)44
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the average of 5 positive integers is 40 and the difference between...
The average of 5 positive integers is 40. i.e., the sum of these integers = 5 * 40 = 200
Let the least of these 5 numbers be x.
Because the range of the set is 10, the largest of these 5 numbers will be x + 10.
If we have to maximize the largest of these numbers, we have to minimize all the other numbers.
That is 4 of these numbers are all at the least value possible = x.
So, x + x + x + x + x + 10 = 200
Or x = 38.
So, the maximum value possible for the largest of these 5 integers is 48.
Choice D is the correct answer.
Most Upvoted Answer
If the average of 5 positive integers is 40 and the difference between...
Given information:
- Average of 5 positive integers is 40.
- Difference between the largest and smallest numbers is 10.
To find:
- Maximum value possible for the largest of these 5 integers.
Solution:
Let's assume the smallest number in the set of 5 integers is x.
Since the difference between the largest and smallest numbers is 10, the largest number can be expressed as x + 10.
We know that the average of the 5 positive integers is 40. Therefore, the sum of these 5 integers is 40 * 5 = 200.
Equation 1: x + (x + 1) + (x + 2) + (x + 3) + (x + 10) = 200
Equation 2: 5x + 16 = 200
Simplifying equation 2, we get:
5x = 200 - 16
5x = 184
x = 36.8
Since the numbers are positive integers, the smallest number (x) must be 37.
The largest number can be expressed as x + 10, which is 37 + 10 = 47.
Therefore, the maximum value possible for the largest of these 5 integers is 47.
Hence, the correct answer is option D) 48.
- Average of 5 positive integers is 40.
- Difference between the largest and smallest numbers is 10.
To find:
- Maximum value possible for the largest of these 5 integers.
Solution:
Let's assume the smallest number in the set of 5 integers is x.
Since the difference between the largest and smallest numbers is 10, the largest number can be expressed as x + 10.
We know that the average of the 5 positive integers is 40. Therefore, the sum of these 5 integers is 40 * 5 = 200.
Equation 1: x + (x + 1) + (x + 2) + (x + 3) + (x + 10) = 200
Equation 2: 5x + 16 = 200
Simplifying equation 2, we get:
5x = 200 - 16
5x = 184
x = 36.8
Since the numbers are positive integers, the smallest number (x) must be 37.
The largest number can be expressed as x + 10, which is 37 + 10 = 47.
Therefore, the maximum value possible for the largest of these 5 integers is 47.
Hence, the correct answer is option D) 48.
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If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?a)50b)52c)49d)48e)44Correct answer is option 'D'. Can you explain this answer?
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