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The maximum mark in an examination is 100 and the minimum is 0. The av
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12 Aug 2021, 07:29
12 Aug 2021, 07:29
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The maximum mark in an examination is 100 and the minimum is 0. The average mark of seven students such that no two of them have scored the same marks is 88. If the median score is 92 and all the marks are integers, what is the maximum possible difference between the highest and the least mark obtained by these seven students?
A. 11
B. 46
C. 99
D. 54
E. 100
A. 11
B. 46
C. 99
D. 54
E. 100
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Re: The maximum mark in an examination is 100 and the minimum is 0. The av
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12 Aug 2021, 07:31
12 Aug 2021, 07:31
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Carcass wrote:
The maximum mark in an examination is 100 and the minimum is 0. The average mark of seven students such that no two of them have scored the same marks is 88. If the median score is 92 and all the marks are integers, what is the maximum possible difference between the highest and the least mark obtained by these seven students?
A. 11
B. 46
C. 99
D. 54
E. 100
A. 11
B. 46
C. 99
D. 54
E. 100
The average mark of seven students such that no two of them have scored the same marks is 88.
This means: (the sum of all seven scores)/7 = 88
Multiply both sides by 7 to get: the sum of all seven scores = 616
The median score is 92
So if we write all seven scores in ascending order, the middlemost score will be 92 as follows: _, _, _, 92, _, _, _
What is the maximum possible difference between the highest and the least mark obtained by these seven students?
In order to maximize the range, we must maximize the biggest number and minimize the smallest number.
Let's start by maximizing the biggest number.
Since the maximum score is 100, our resulting set looks like this: _, _, _, 92, _, _, 100
At this point we want to minimize the smallest value.
Since the sum of all seven scores = 616, we want to maximize the value of every score except the smallest score.
When we do this we get: _, 90, 91, 92, 98, 99, 100
The sum of the 6 biggest numbers = 90 + 91 + 92 + 98 + 99 + 100 = 570
So, the last remaining number (the smallest number) = 616 - 570 = 46
So the seven scores are as follows: 46, 90, 91, 92, 98, 99, 100
Range = biggest - smallest = 100 - 46 = 54
Answer: D
Re: The maximum mark in an examination is 100 and the minimum is 0. The av
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24 Jan 2022, 03:13
24 Jan 2022, 03:13
Instead of maximizing the number, can I start with minimizing the number? As 1,2,3,92,.. Will I get the right answer?
The average mark of seven students such that no two of them have scored the same marks is 88.
This means: (the sum of all seven scores)/7 = 88
Multiply both sides by 7 to get: the sum of all seven scores = 616
The median score is 92
So if we write all seven scores in ascending order, the middlemost score will be 92 as follows: _, _, _, 92, _, _, _
What is the maximum possible difference between the highest and the least mark obtained by these seven students?
In order to maximize the range, we must maximize the biggest number and minimize the smallest number.
Let's start by maximizing the biggest number.
Since the maximum score is 100, our resulting set looks like this: _, _, _, 92, _, _, 100
At this point we want to minimize the smallest value.
Since the sum of all seven scores = 616, we want to maximize the value of every score except the smallest score.
When we do this we get: _, 90, 91, 92, 98, 99, 100
The sum of the 6 biggest numbers = 90 + 91 + 92 + 98 + 99 + 100 = 570
So, the last remaining number (the smallest number) = 616 - 570 = 46
So the seven scores are as follows: 46, 90, 91, 92, 98, 99, 100
Range = biggest - smallest = 100 - 46 = 54
Answer: D
GreenlightTestPrep wrote:
Carcass wrote:
The maximum mark in an examination is 100 and the minimum is 0. The average mark of seven students such that no two of them have scored the same marks is 88. If the median score is 92 and all the marks are integers, what is the maximum possible difference between the highest and the least mark obtained by these seven students?
A. 11
B. 46
C. 99
D. 54
E. 100
A. 11
B. 46
C. 99
D. 54
E. 100
The average mark of seven students such that no two of them have scored the same marks is 88.
This means: (the sum of all seven scores)/7 = 88
Multiply both sides by 7 to get: the sum of all seven scores = 616
The median score is 92
So if we write all seven scores in ascending order, the middlemost score will be 92 as follows: _, _, _, 92, _, _, _
What is the maximum possible difference between the highest and the least mark obtained by these seven students?
In order to maximize the range, we must maximize the biggest number and minimize the smallest number.
Let's start by maximizing the biggest number.
Since the maximum score is 100, our resulting set looks like this: _, _, _, 92, _, _, 100
At this point we want to minimize the smallest value.
Since the sum of all seven scores = 616, we want to maximize the value of every score except the smallest score.
When we do this we get: _, 90, 91, 92, 98, 99, 100
The sum of the 6 biggest numbers = 90 + 91 + 92 + 98 + 99 + 100 = 570
So, the last remaining number (the smallest number) = 616 - 570 = 46
So the seven scores are as follows: 46, 90, 91, 92, 98, 99, 100
Range = biggest - smallest = 100 - 46 = 54
Answer: D
