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Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the

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delta09
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Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   16 Dec 2009, 02:37
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Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?

A. 3
B. 5
C. 7
D. 8
E. 9

OPEN DISCUSSION OF THIS QUESTION IS HERE: given-distinct-positive-integers-1-11-3-x-2-and-9-whic-109801.html
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   23 Nov 2016, 02:27
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delta09 wrote:
Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?

A. 3
B. 5
C. 7
D. 8
E. 9


The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.

Arrange numbers in ascending order: 1, 2, 3, 9, 11, and x.

Now, x can not possibly be less than 3 as given that all integers are positive and distinct (and we already have 1, 2, and 3).

Next, if x is 3<x<9 then the median will be the average of 3 and x. As all answers for the median are integers, then try odd values for x:
If x=5, then median=(3+5)/2=4 --> not among answer choices;
If x=7, then median=(3+7)/2=5 --> OK;

Answer: B.

P.S. If x is more than 9 so 10 or more then the median will be the average of 3 and 9 so (3+9)/2=6 (the maximum median possible).

OPEN DISCUSSION OF THIS QUESTION IS HERE: given-distinct-positive-integers-1-11-3-x-2-and-9-whic-109801.html
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   16 Dec 2009, 03:01
delta09 wrote:
Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?

a)3
b)5
c)9
d)8
e)7


arranging the series we have 1,2,3,9,11 and x after 3 and anywhere b/w 3,9,11 or after 11.

a-3 cannot be the median as we have 6 elements in set
b -5 possible if x= 7
c- 9 not possible
d- 8 not possible
e- 7 not possible
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   16 Dec 2009, 03:09
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The answer would be b 5.
Here arranging the numbers in the ascending order
1,2,3,9,11 and x
Here the median can be <3 or >9 or in between 3 and 9.
X <3 is not possible as given integers are positive and distinct and 0 is neither positive nor negative
X >9 => median would be 6 which is not present in the list of answer choices
the answer would be the average of two numbers.
answer cannot be 3 or 9 as the given integers are distinct
x between 3 and 9 => the median is the average of 3 and x
the answers choices left are 5,8,7
for 7 to be median x should be 2*7-3=11
for 8 to be median x should be 2*8-3=13
11 and 13 are not in the range 3-9 so the answer choice left is 5 with the value of x as 7
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   31 Jan 2010, 13:12
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delta09 wrote:
Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?

a)3
b)5
c)9
d)8
e)7


The number can only be arranged in this manner...

1,2,3,x,9,11..... reason..... if we consider 1,2,3,9,x,11... or 1,2,3,9,11,x.... the median is anyway 6 which is not present in the list...

Hence sequence to consider is: 1,2,3,x,9,11...

plug in the values in increasing order.... would save time...

(x+3)/2 = 3 gives x = 3... which is not possible.... .. (already present..)
(x+3)/2 = 5 gives x = 7... which is possible....
(x+3)/2 = 7 gives x = 11... which is not possible.... (already present..)
(x+3)/2 = 8 & (x+3)/2 = 9 can be avoided as this would increase the value of x more than 11... which would again turn the median to be 6.. which isnt correct...

Therefore answer is B...
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink] New post   23 Nov 2016, 00:31
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delta09 wrote:
Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the following could be the median?

a)3
b)5
c)9
d)8
e)7



Arranging in increasing order

1, 2, 3, 9, 11 and x has to come somewhere in the sets of numbers

If x<2, then Median = Average of 2 and 3 = 2.5
If x>9, then Median = Average of 3 and 9 = 6

So median must lie between 2.5 and 6

But since numbers are distinct so median can never be 3 (for median to be 3 x should be 3 as well which is not acceptable due to terms being distinct)

Hence Answer: Option B
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Re: Given distinct positive integers 1, 11, 3, x, 2, and 9, which of the [#permalink]
23 Nov 2016, 00:31
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