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A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increa
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12 Aug 2021, 07:28
12 Aug 2021, 07:28
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A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
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Re: A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increa
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12 Aug 2021, 07:37
12 Aug 2021, 07:37
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Carcass wrote:
A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
(A) -1
(B) 0
(C) 1
(D) 2
(E) Cannot be determined.
First off, the question tells us that the numbers are arranged in ascending order.
So, we know that x ≤ -8, and y ≥ 9
There are 8 elements in the set. So, the median = the average of the two middlemost values.
Here, the two middlemost values are -4 and 4
So, the median = (-4 + 4)/2 = 0/2 = 0
Since the median and the mean of the set are EQUAL, we know that the mean is also 0
That is, [x + (-8) + (-5) + (-4) + 4 + 6 + 9 + y]/8 = 0
Multiply both sides by 8 to get: x + (-8) + (-5) + (-4) + 4 + 6 + 9 + y = 0
Simplify: x + y + 2 = 0
This means x + y = -2
So, here's what we know:
x + y = -2
x ≤ -8
y ≥ 9
Let's find some values of x and y and see where this leads us....
x = -12 and y = 10
In this case, |x|-|y|= |-12|-|10| = 12 - 10 = 2
x = -13 and y = 11
In this case, |x|-|y|= |-13|-|11| = 13 - 11 = 2
x = -12.5 and y = 10.5
In this case, |x|-|y|= |-12.5|-|10.5| = 12.5 - 10.5 = 2
x = -100 and y = 98
In this case, |x|-|y|= |-100|-|98| = 100 - 98 = 2
As we can see, the answer will always be 2
Answer: D
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Re: A set S = {x, -8, -5, -4, 4, 6, 9, y} with elements arranged in increa
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16 Oct 2022, 03:07
16 Oct 2022, 03:07
As we can see when all numbers are added, they cancel each other and we are left with +2, thus we need to choose x and y values such that mean and median do not change in addition to that y is either >= 9. Also we need to choose x value such that it cancels out additional 2 and is also less than -8. A possible choice is y=9, and x=-11
This gives |x|-|y| = 11-9 =2
This gives |x|-|y| = 11-9 =2
