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30 Jun 2022, 07:15
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S is a set containing 7 distinct positive integers. If the mean of S is 13 and the median of S is 6, what is the largest possible value of the greatest element of S?
A) 42
B) 58
C) 64
D) 70
E) 85
A) 42
B) 58
C) 64
D) 70
E) 85
30 Jun 2022, 09:22
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Given that S is a set containing 7 distinct positive integers and the mean of S is 13 and the median of S is 6 and we need to find the largest possible value of the greatest element of S
Now, Mean = 13
=> Sum = Mean * 7 (As there are 7 numbers) = 13*7 = 91
Since, Median (=6) is the middle term of the set
=> Median is\( \frac{7+1}{2}^th \) term = \(4^th\) term = 6
So, the set is _ , _ , _, 6 , _ , _ , _ => 3 numbers are smaller than 6 and 3 are greater than 6
Now, it is given to us that all 7 numbers are distinct positive integers and we need to find the largest possible value of the greatest number
=> We need to take least possible value for all other numbers
So, we can take the numbers as 1,2,3,6,7,8,X
1,2,3 because they are the least distinct positive integers
7,8 because they are just greater than 6 and are distinct
=> Sum = 91
=> 1 + 2 + 3 + 6 + 7 + 8 + X = 91
=> X = 91 - 27 = 64
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Now, Mean = 13
=> Sum = Mean * 7 (As there are 7 numbers) = 13*7 = 91
Since, Median (=6) is the middle term of the set
=> Median is\( \frac{7+1}{2}^th \) term = \(4^th\) term = 6
So, the set is _ , _ , _, 6 , _ , _ , _ => 3 numbers are smaller than 6 and 3 are greater than 6
Now, it is given to us that all 7 numbers are distinct positive integers and we need to find the largest possible value of the greatest number
=> We need to take least possible value for all other numbers
So, we can take the numbers as 1,2,3,6,7,8,X
1,2,3 because they are the least distinct positive integers
7,8 because they are just greater than 6 and are distinct
=> Sum = 91
=> 1 + 2 + 3 + 6 + 7 + 8 + X = 91
=> X = 91 - 27 = 64
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
