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The terms of each set above are given in ascending order. If the media

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Bunuel
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The terms of each set above are given in ascending order. If the media [#permalink] New post   01 Apr 2016, 03:56
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Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2
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B
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RDhin
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Re: The terms of each set above are given in ascending order. If the media [#permalink] New post   01 Apr 2016, 04:33
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Bunuel wrote:
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2


So we have even no. of elements in the Set

So median is the average of Middle two numbers
(x+8)/2= (y+9)/2
y - x= -1

Answer B
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BrentGMATPrepNow
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The terms of each set above are given in ascending order. If the media [#permalink] New post   Updated on: 17 May 2021, 07:36
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Bunuel wrote:
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2


Key property: When we have an EVEN number of terms, the median of those terms will be the AVERAGE of the two middlemost terms, when those terms are listed in ascending order

So the median of Set A = (x + 8)/2
And the median of Set B = (y + 9)/2

Since we're told that the two medians are equal, we can write: (x + 8)/2 = (y + 9)/2
Multiply both sides of the equation by 2 to get: x + 8 = y + 9
Subtract x from what sides to get: 8 = y - x + 9
Subtract 9 from both sides to get: -1 = y - x

Answer: B

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Originally posted by BrentGMATPrepNow on 09 Feb 2020, 09:15.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:36, edited 1 time in total.
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Re: The terms of each set above are given in ascending order. If the media [#permalink] New post   03 Sep 2020, 07:17
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Given

    • Set A: 3, x, 8, 10 and Set B: 4, y, 9, 11
    • The terms of each set above are given in ascending order and the median of Set A is equal to the median of Set B.


To Find

    • The value of y – x.


Approach and Working Out

    • 3, x, 8, 10 will have a median of \(\frac{(x + 8)}{2}\)
    • 4, y, 9, 10 will have a median of \(\frac{(y + 9)}{2}\)

    • \(\frac{(x + 8)}{2}\) = \(\frac{(y + 9)}{2}\)
      o x + 8 = y + 9
      o y – x = 8 – 9 = -1


Correct Answer: Option B
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Re: The terms of each set above are given in ascending order. If the media [#permalink] New post   03 Sep 2020, 11:43
Bunuel wrote:
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2


\(x + 8 = y + 9\) { Ignoring common division by 2 both on LHS and RHS }

Or, \(y -x = -1\) , Hence Answer must be (B)
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Re: The terms of each set above are given in ascending order. If the media [#permalink] New post   11 Sep 2020, 14:06
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Bunuel wrote:
Set A: 3, x, 8, 10
Set B: 4, y, 9, 11

The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – x?

A. -2
B. -1
C. 0
D. 1
E. 2

Solution:

The median of set A is (x + 8)/2 and the median of set B is (y + 9)/2. Since they two medians are equal, we can create the equation:

(x + 8)/2 = (y + 9)/2

x + 8 = y + 9

-1 = y - x

Answer: B
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Re: The terms of each set above are given in ascending order. If the media [#permalink] New post   12 Sep 2020, 00:52
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Set A: 3, x, 8, 10 and Set B: 4, y, 9, 11

Median of Set A: \(\frac{(x + 8) }{ 2}\)

Median of Set B: \(\frac{(y + 9) }{ 2}\)


Median of Set A = Median of Set B

=> \(\frac{(x + 8) }{ 2}\) = \(\frac{(y + 9) }{ 2}\)

=> (x + 8) = ( y + 9)

=> y - x = -1

Answer B
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Re: The terms of each set above are given in ascending order. If the media [#permalink]
12 Sep 2020, 00:52
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