Median

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In this question, im not clear why we cant take 4 as X in that case wont the median be 3?

Thanks

[Uva@90]

Hi Shibsriz,
if X =4 then set will be 2,4,5,9.
Median = (4+5)/2 =4.5
how you got 3 ?

Regards,
Uva.

[GMATGuruNY]

In this question, im not clear why we cant take 4 as X in that case wont the median be 3?

Thanks

Eliminate the four answer choices that COULD be the median.

2, 2, 5, 9 --> median = (2+5)/2 = 3.5.
Eliminate B.

2, 3, 5, 9 --> median = (3+5)/2 = 4.
Eliminate C.

2, 5, 5, 9 --> median = (5+5)/2 = 5.
Eliminate D.

2, 5, 8, 9 --> median = (5+8)/2 = 6.5.
Eliminate E.

The correct answer is A.

Of the 3 given values -- 2, 5, and 9 -- the average of the two smallest = (2+5)/2 = 3.5.
Implication:
The median cannot be less than 3.5.
To illustrate:
The least possible value for X is 1.
If X = 1, then the set becomes {1, 2, 5, 9}, in which case the median = (2+5)/2 = 3.5.

[sanju09]

In this question, im not clear why we cant take 4 as X in that case wont the median be 3?

Thanks

Median is 3.0 if the sum of two middle integers is 6, and X, 2, 5, 9 may be the order if X = 1 or 2, median is not 3.0. Further, 2, X, 5, 9 may be the order if X = 3, 4 or 5, median is not 3.0.Continue, 2, 5, X, 9 may be the order if X = 5, 6, 7, 8, or 9, median is not 3.0. Finally, 2, 5, 9, X may be the order if X = 9 or more, median is not 3.0, because median cannot be 3.0 in the given scenario. Not interested in testing remaining choices because I love A.

If X = 4, order is 2, 4, 5, 9 and the median is 4.5, not 3.0.

Revision: To determine median, we must list the numbers in order first, next count them, if they are 5 (means odd), the median will be ½ (5 + 1)th i.e. 3rd term from left or right, and if they are 4 (means even), there occur two medians, one is 4/2th i.e. 2nd term and the other is the next, means the 3rd term. The absolute median in this case is the average (arithmetic mean) of the two medians.

[theCodeToGMAT]

(x,2,5,9)

For Even number of array, Median = (Middle 1 + Middle 2)/2

Since, "5" will always be there so.. (5+Middle2)/2

{A} 3.0 ==> 3.0 = (5+Middle2)/2 ==> Middle2 = 1 ==> NOT POSSIBLE
{B} 3.5 ==> 3.5 = (5+Middle2)/2 ==> Middle2 = 2 ==> POSSIBLE
{C} 4.0 ==> 4.0 = (5+Middle2)/2 ==> Middle2 = 3 ==> POSSIBLE
{D} 5.0 ==> 5.0 = (5+Middle2)/2 ==> Middle2 = 5 ==> POSSIBLE
{E} 6.5 ==> 6.5 = (5+Middle2)/2 ==> Middle2 = 8 ==> POSSIBLE

[spoiler]{A}[/spoiler]