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

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24 Nov 2008, 18:37

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Difficulty:

35% (medium)

Question Stats:

73% (00:07) correct
27% (01:07) wrong based on 26 sessions

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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

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

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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.
_________________

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

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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.

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

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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