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

Question

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

RDhin · Answer

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

BrentGMATPrepNow · Answer

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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EgmatQuantExpert · Answer

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

Abhishek009 · Answer

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

Or,  y -x = -1  ,  Hence Answer must be (B)

ScottTargetTestPrep · Answer

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

MathRevolution · Answer

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

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

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