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

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For the set of terms shown above, if y > 6 and the mean of [#permalink]  02 Nov 2009, 03:08
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Question Stats:

62% (03:28) correct 38% (02:15) wrong based on 149 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2012, 15:59, edited 1 time in total.
Edited the question and added the OA
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Re: Sequence [#permalink]  02 Nov 2009, 10:22
1
This post was
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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

(x + y) 2

y + 3

y

3y/2

x /3 + y

adding up all the elements of set we get
(3x + xy)/6 = y+3 => solving this we get x=6
we have y>6 so we get
x=6,y>6,x+y >12, x-4y < -18,xy>36 and 2y >12
arranging these we get x-4y, x, y, x+y, 2y, xy

median = (y + x+y) /2 = (2y+6)/2 = y+3
will go with option 2
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Re: Sequence [#permalink]  02 Nov 2009, 11:22
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

(x + y) 2

y + 3

y

3y/2

x /3 + y

I get:

(x + y + x + y + x - 4y + xy + 2y)/6 = y + 3

Combine like terms and you get:

3x + xy = 6y + 18
x(3+y)=6(y+3)
3+y cancel
x = 6

Substitute 6 for x in the above equation
Also, since y>6 pick any number for y and solve. Let's say I pick a 7

the following six numbers are:
6, 7, 13, -22, 42, 14

median = (7+13)/2 = 10

my answer is B = y + 3
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Re: Sequence [#permalink]  11 Feb 2012, 15:33
Find the average and set it equal to the y+3 then find out that x=6
then you find that y and x+y are the middle 2 numbers and sub x for 6 then you find the median number is y+3
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Re: Sequence [#permalink]  11 Feb 2012, 15:57
1
KUDOS
Expert's post
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.

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.

Hope it helps.
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Kudos [?]: 257 [0], given: 11

For the set of terms shown above, if y > 6 and the mean of the s [#permalink]  12 Dec 2012, 23:05
x y, x + y, x – 4y, xy, 2y

$$\frac{{x + y + (x+y) + (x-4y) + xy + 2y}}{{6}} = y+3$$
$${x + y + (x+y) + (x-4y) + xy + 2y}=6(y+3)$$
$$3x + xy = 6(x+y)$$
$$x(y+3)=6(3+y)$$
$$x=6$$

Let y=7 and x=6: Set={-18, 6, 7, 13, 14, 42}
Thus, median is \frac{(7+13)}{2} = 10

A. (x + y)/2 = 13/2
B. y + 3 = 10
C. y = 7
D. (3y)/2 = 21/2
E. x/3 + y = 9

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Re: For the set of terms shown above, if y > 6 and the mean of [#permalink]  14 Oct 2014, 04:37
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Re: For the set of terms shown above, if y > 6 and the mean of [#permalink]  15 Apr 2015, 20:20
Bunuel wrote:
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.

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.

Hope it helps.

Hi Bunuel,

Just a small clarification needed. The highlighted portion: Is it implying that (y+3) on both sides cannot be discarded? if so, then why exactly because as per my understanding when the term in question can be ZERO, only then we must avoid cancelling it on both LHS and RHS.
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Re: For the set of terms shown above, if y > 6 and the mean of [#permalink]  16 Apr 2015, 07:02
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

assume y = 7

x would come out to be 6 (as mean is given)

median = 10

option b satisfies.
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Re: For the set of terms shown above, if y > 6 and the mean of   [#permalink] 16 Apr 2015, 07:02
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