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GRE Math Challenge #11 - Set A: {x, x, x, y, y, y, 3x+y, x–y

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soumya1989
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GRE Math Challenge #11 - Set A: {x, x, x, y, y, y, 3x+y, x–y [#permalink] New post   15 Sep 2014, 13:42
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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?

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40
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Re: GRE Math Challenge #11 [#permalink] New post   15 Sep 2014, 13:45
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Explanation


If we arrange the numbers from the smallest to the highest order the order will be the following-
{x-y,x,x,x,y,y,y,3x+y}

So the median is \(\frac{(x+y)}{2}\)=10. ie, x+y =20.

The range is \((3x+y)-(x-y)\)= 2(x+y). therefore = 2*20= 40 [Ans]
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Re: GRE Math Challenge #11 [#permalink] New post   15 May 2015, 11:37
Great solution, Soumya!
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Set A: {x, x, x, y, y, y, 3x+y, x–y } If the median of set [#permalink] New post   15 Oct 2017, 22:59
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?

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Show: :: OA
40


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Re: Set A: {x, x, x, y, y, y, 3x+y, x–y } If the median of set [#permalink] New post   15 Oct 2017, 23:46
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Using the fact that x<y, we can order our set increasingly as {x-y x x x y y y 3x-y}. Then, the fact that the median is 10 can be rewritten as (x+y)/2 = 10 or x+y = 20.

The range of the set is computed as 3x-y-(x-y) = 2x+2y = 2(x+y) = 2*20 = 40.

The range is 40!
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Re: GRE Math Challenge #11 - Set A: {x, x, x, y, y, y, 3x+y, x–y [#permalink] New post   16 Feb 2020, 17:38
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Re: GRE Math Challenge #11 - Set A: {x, x, x, y, y, y, 3x+y, xy [#permalink] New post   16 Jun 2023, 14:15
Solved in 1:30

We are given the median. Since A is composed of 9 numbers, the median will be the average of the 4th and 5th value.
So we need to find the 4th and 5th value.
We know that x-y must be some negative number, so it will be the first
then all the xs, then all the ys, and then 3x+y
the 4th value is x, and 5th value is y.
So we know that (x+y)=20
the range is (max-min)=(3x+y-(x-y))=(2x+2y)
we know that x+y, so twice that is just 40
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Re: GRE Math Challenge #11 - Set A: {x, x, x, y, y, y, 3x+y, xy [#permalink]
16 Jun 2023, 14:15
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