Source: Magoosh
Set A:\(\{x, x, x, y, y, y, 3x+y, x-y\}\)
If the median of set A is 10 and \(0 < x < y\), what is the range of set A?
A. 10
B. 20
C. 30
D. 40
E. 60
The OA is D
If the median of set A is 10 and 0 < x < y, what is th
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- Jay@ManhattanReview
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Given \(0 < x < y\), we know that both x and y are positive and y is greater than x. Thus, the smallest number in Set A would be x - y and the largest would be 3x + y. Thus, range = (3x + y) - (x - y) = 2(x + y).BTGmoderatorLU wrote:Source: Magoosh
Set A:\(\{x, x, x, y, y, y, 3x+y, x-y\}\)
If the median of set A is 10 and \(0 < x < y\), what is the range of set A?
A. 10
B. 20
C. 30
D. 40
E. 60
The OA is D
Arranging the elements of Set A, we get \(\{x-y, x, x, x, y, y, y, 3x+y\}\). There are 8 elements in the set. The median would be average of the 4th and 5th elements = (x + y)/2
Thus, (x + y)/2 = 10 => x + y = 20
Thus, range = 2(x + y) = 2*20 = 40.
The correct answer: D
Hope this helps!
-Jay
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Since both x and y are positive, x - y will be the smallest element, and 3x + y will be the largest element of set A.BTGmoderatorLU wrote:Source: Magoosh
Set A:\(\{x, x, x, y, y, y, 3x+y, x-y\}\)
If the median of set A is 10 and \(0 < x < y\), what is the range of set A?
A. 10
B. 20
C. 30
D. 40
E. 60
The OA is D
Since x < y, in ascending order, we have:
x - y, x, x, x, y, y, y, 3x + y.
Since the median is 10, we have (x + y)/2 = 10 or x + y = 20.
The range of set A is:
3x + y - (x - y) = 2x + 2y = 2(x + y) = 2(20) = 40.
Answer: D
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