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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.
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.
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:
- Average of 5 positive integers = 40
- Difference between the largest and the smallest of these 5 numbers is 10
To find:
- Maximum value possible for the largest of these 5 integers
Approach:
- Let the smallest of the 5 integers be x
- Then, the largest of the 5 integers will be (x+10)
- We can use this information to form an equation in x
- Solve for x
- Then, calculate the value of (x+10) to get the maximum possible value for the largest integer
Calculation:
- According to the given information, the sum of the 5 integers is (5*40) = 200
- Let the smallest of the 5 integers be x
- Then, the sum of the remaining 4 integers will be (200 - x)
- Also, the largest integer will be (x+10)
- Since the average of the 5 integers is 40, we have:
- (Sum of 5 integers) / 5 = 40
- 200 / 5 = 40
- Sum of 5 integers = 200
- Using the information above, we can form an equation in x:
- x + (x+1) + (x+2) + (x+3) + (x+10) = 200
- 5x + 16 = 200
- 5x = 184
- x = 36.8
- Since x has to be a positive integer, we can round it up to 37
- Therefore, the largest integer will be (x+10) = 47
- Hence, the maximum value possible for the largest of these 5 integers is 47
Answer:
- Option (d) 48 is incorrect
- Option (e) 44 is lower than the maximum possible value for the largest integer
- Option (c) 49 is higher than the maximum possible value for the largest integer
- Option (a) 50 is higher than the maximum possible value for the largest integer
- Option (b) 52 is higher than the maximum possible value for the largest integer
- Therefore, the correct answer is option (d) 47
- Average of 5 positive integers = 40
- Difference between the largest and the smallest of these 5 numbers is 10
To find:
- Maximum value possible for the largest of these 5 integers
Approach:
- Let the smallest of the 5 integers be x
- Then, the largest of the 5 integers will be (x+10)
- We can use this information to form an equation in x
- Solve for x
- Then, calculate the value of (x+10) to get the maximum possible value for the largest integer
Calculation:
- According to the given information, the sum of the 5 integers is (5*40) = 200
- Let the smallest of the 5 integers be x
- Then, the sum of the remaining 4 integers will be (200 - x)
- Also, the largest integer will be (x+10)
- Since the average of the 5 integers is 40, we have:
- (Sum of 5 integers) / 5 = 40
- 200 / 5 = 40
- Sum of 5 integers = 200
- Using the information above, we can form an equation in x:
- x + (x+1) + (x+2) + (x+3) + (x+10) = 200
- 5x + 16 = 200
- 5x = 184
- x = 36.8
- Since x has to be a positive integer, we can round it up to 37
- Therefore, the largest integer will be (x+10) = 47
- Hence, the maximum value possible for the largest of these 5 integers is 47
Answer:
- Option (d) 48 is incorrect
- Option (e) 44 is lower than the maximum possible value for the largest integer
- Option (c) 49 is higher than the maximum possible value for the largest integer
- Option (a) 50 is higher than the maximum possible value for the largest integer
- Option (b) 52 is higher than the maximum possible value for the largest integer
- Therefore, the correct answer is option (d) 47
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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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