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Set S includes elements {8, 2, 11, x, 3, y} and has a mean

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Manager
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Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 24 Nov 2008, 18:37
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If you know how to solve the following problem and you can explain your answer, please let me know. thanks!

Set S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
a)0
b)1
c)2
d)3
e)4

The OA is d
[Reveal] Spoiler: OA

Last edited by JarvisR on 26 Jul 2015, 19:25, edited 2 times in total.
Moved it under correct forum and updated the tag.

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 24 Nov 2008, 19:22
Remove x and y from the set. So remaining set is {2, 3, 8, 11}.

Mean of whole set is 7. that means 2+3+8+11+x+y/6 = 7
=> x+y = 42 - 24 = 18..............(1)

Since there are even number of elements in the set so mode will be average of middle two terms, when elements are ordered in ascending terms.

Say middle terms are m1 and m2, so m1+m2/2 = 5.5 => m1+m2 = 11....(2)

Since x needs to be maximized, say we take x=8 then y = 10
Set = {2,3,8,8,10,11} Eq. 1 satisfied but 2 Not.

Similarly keep on reducing x by 1 and increase y by 1. You will see that at x = 3 both Eq. 1 and 2 are satisfied.

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 24 Nov 2008, 22:27
GMAT_700 wrote:
Set S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
a)0
b)1
c)2
d)3
e)4


D. First, it is not advisable to revel the OA with the question.
sum = 7x6 = 42
x + y = 42 - (2+3+8+11) = 42

Since y > x, the median is 5.5, and x is a possible max., we need to divide 18 between x and y so that the previous conditions are met. The sum of the 3rd (t) and 4th (f) terms in acending orders is 11. how this is possible? the followings are the two most likely possible ways to arrange the elements of the set.

A: {2, 3, 8, x, y, 11} :- not possibnle cuz median is not 5.5.
B: {2, 3, x, 8, 11, y} :- could be possible if x is 3.
C: {2, x, 3, 8, 11, y} :- could be possible but violates the constraints that x has to be max. so no better than B.
D: {x, 2, 3, 8, 11, y} :- same as C.

so B looks reasonable. if so x has to be 3.
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Manager
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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 25 Nov 2008, 00:12
echo that explanation...
i rem seeing a very similar problem in OG11 as well....

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Schools: Stanford...Wait, I will come!!!
Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 25 Nov 2008, 02:35
prasun84 wrote:
echo that explanation...
i rem seeing a very similar problem in OG11 as well....

S={8,2,11,x,3,y}
Mean is 7, it implies..as above..
x+y=18

Now, here ..i have got different view.
Median is 5.5 ... as there are 6 numbers...
so.. order of the number can be like this..
2,3,x,8,11,y
x,2,3,8,11,y
As, we don't know if x and y are integers and positive integer, then there are many other combination.
but, the value of x cannot be more than 8 for median to be 5.5.
so..if x is positive.. or equal to 0, then minimum value is 0. and y=18.
increase value of x by 1.. we will find that..
when x=3,
the order is
2,3,3,8,11,15
if we increase the value of x by 1 more,
2,3,4,8,11,15...the median becomes 6..
so..maximum value of x can be 3.

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 25 Nov 2008, 21:35
We can see that : x+y=18
otherwise x<y so y definitely >9 and y's position is on the right of 8.(2,3...,8,y...)( of course we don't know whether y greater than 11 or not).
From this, we can see 8 is the third or the fourth element of S.(1)
The Median is 11, and it must be the sum of the third and the fourth elements of S.We have 8+a=11 so a=3.
If x>8 then 8 is 3rd and x is 4th, x=3 >8--> ridiculous
if x<8 then 8 is 4th, and x or 3 maybe the 3rd.So x<= 3=a

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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New post 25 Nov 2008, 21:41
Agree. Same explanation

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean   [#permalink] 25 Nov 2008, 21:41
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