For the set of terms shown above, if y 6 and the mean of t

Question

x, y, x + y, x - 4y, xy, 2y For the set of terms shown above, if y > 6 and the mean of the set equals y + 3, then the median must be A. (x+y)/2 B. y+3 C. y D. 3y/2 E. x/3+y OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-set-of-terms-shown-above-if-y-6-and-the-mean-of-86182.html

asterixmatrix · Answer

when we add all the terms we get (3x+xy)/6 = y+3 hence x=6

x=6 and y>6 (given)
x+y>12
x-4y is -ve
xy = 6y
2y> 12 which is greater than x+y as x=6

so we can arrange it as x-4y, x,y,x+y,2y,5y.
Median is  /2 = (2y+6)/3...so Ans Option B

Edited the number of terms from 5 to 6.

Asterix
Imagine if Gauls were so silly what would Romans had done.... given them a GMAT question!!!!

srini123 · Answer

Following approach as detailed by astermatrix,

the sequence would be x-4y, x,y,x+y, 2y,5y

and median would be \frac{y+x+y}{2} = \frac{x}{2} + y

since x=6

the answer is y + 3

ngoctraiden1905 · Answer

average= (3x+xy)/6=y+3
=> (y+3) (x-6)=0
=> x=6 because y>6
Can arrange the set in the following order:
(x-4y,x,y,x+y,2y,xy)
median= (y+x+y)/2=y+x/2 = y+3 ok

amit2k9 · Answer

x = 6 solving the means and sum equation.
taking y = 10 gives median = 13

B fits

subhashghosh · Answer

x + y + x + y + x – 4y + xy + 2y = 6(y+3)

=> 3x + xy = 6(y+3)

=> x = 6

So the set is in ascending order :

x - 4y, x, y, x+y, 2y, xy

Median = (x + 2y)/2 = 3 + y

Answer - B

Nayimoni · Answer

We can calculate the mean as Sum / count which means 3x + xy /6 = y +3 or x(3+y)=6(y+3). After recognizing this manipulation, we deduce x =6 and we have y = GT(6).

Using this information, we can arrange in increasing order to find the median. Note the count is even so the median is the average of the two middle terms.

The arranged increasing set on the number line is: 6 -4y ; 6 ; y ; 6 + y ; 2y ; 6y

The two middle terms are are y and 6 +y, so the average is 6+2y /2 or 3 + y.

Answer is B

Bunuel · Answer

x, y, x + y, x - 4y, xy, 2y
For the set of terms shown above, if y > 6 and the mean of the set equals y + 3, then the median must be
A. (x+y)/2
B. y+3
C. y
D. 3y/2
E. x/3+y

First of all: the median of a set with even # of terms is the average of two middle terms (when ordered in ascending/descending order).

Next, given that the mean of the set equals y+3: x+y+(x+y)+(x-4y)+xy+2y=6*(y+3) --> 3x+xy=6*(y+3) --> x(3+y)=6(y+3), notice that generally you cannot reduce by 3+y here as suggested above --> (3+y)(x-6)=0 --> x=6 or y=-3 (not a valid solution as y>6), so x=6;

Arrange the set in ascending order: {x-4y, x, y, x+y, 2y, xy} --> median=(y+x+y)/2=(2y+6)/2=y+3.

Answer: B.

Or: pick some number greater than 6 for y, let's say y=7. Then our set will be: {6, 7, 13, -22, 42, 14} --> arrange in ascending order: {-22, 6, 7, 13, 14, 42}.

Thus the median of the set is (7+13)/2=10 --> 10=7+3=y+3.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-the-set-of-terms-shown-above-if-y-6-and-the-mean-of-86182.html

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For the set of terms shown above, if y > 6 and the mean of t

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