If set S consists of the numbers 1, 5, -2, 8, and n, is 0< n< 7?

(1) The median of the numbers in S is less than 5.
(2) The median of the numbers in S is greater than 1.

Source: GMatPrepTest
OA = C

I chose D because of this thought process:
I rearrange set S to: -2, 1, 5, 8 then where can I put n?

from (1), n has to be between 1 and 5-. So 1<n<5- --> SUFF

from (2), n has to be between 1+ and 5, So 1+<n<5 --> SUFF

Can someone please help where I go wrong?

Thanks

The median is defined as the central value( after arranging data in ascending/descending order).

eg: 1,5,45 ----Here the median is 5
eg: -82,-15,45---Here the median is -15

Coming to the problem..

This is correct.

This is Wrong:

From Statement 1:The median of the numbers in S is less than 5.
This means the median can anything less than 5
Case 1:Let n=3;
eg:-2, 1,3,5,8---Here the median is 3( Which is less than 5) and (n=3) is between 0 and 7. Thus Yes( This is a Yes/ No type DS question)
Case 2: Let n=-100;
eg:-100,-2, 1,5,8------Here the median is 1 ( Which is less than 5) and (n=-100) is not between 0 and 7.Thus No
Hence Statement 1 is not sufficient.


This is also Incorrect:
Moving on to Statement 2:The median of the numbers in S is greater than 1.
Case 1:Let n=3;
eg:-2, 1,3,5,8---Here the median is 3( Which is greater than 1) and (n=3) is between 0 and 7. Thus Yes
Case 2: Let n=100;
eg:-2,1,5,8,100,-------Here the median is 5 ( Which is greater than 1) and (n=100) is not between 0 and 7.Thus No
Hence Statement 2 is not sufficient.

Combining both Statements together,
The median of the numbers should be between 1 and 5.
Mathematically, 1<Median<5
Try for extreme cases here ( You can also opt for the conventional method by checking values that satisfy the condition)
Case 1: Try putting n=( More than 7). eg: n=8
ie; -2,1,5,8,8...For all cases where n>=7, the median will be 5. But as per our condition 1<Median<5.
Case 2: Try putting n=(Less than 0). eg: n=-1
ie;-2,-1,1,5,8...For all cases where n<=0, the median will be 1 , which again violates our condition of 1<Median<5.

Therefore,Only values of n where 0< n< 7, will satisfy 1<Median<5. Hence answer is C.

the above poster has produced a nice solution involving number plugging; here is a more intuitive solution.

consider the five different positions in which n could be placed:
(POSITION 1: n < -2)
-2
(POSITION 2: -2 < n < 1)
1
(POSITION 3: 1 < n < 5)
5
(POSITION 4: 5 < n < 8)
8
(POSITION 5: n > 8)
note that, in addition to these five positions, n could also be chosen to be equal to any of the four numbers -2, 1, 5, 8, since there is no conditions stating that the five numbers must be distinct from each other.

let's examine the statements with respect to these five positions.


If set S consists of the numbers 1, 5, -2, 8, and n, is 0< n< 7?


this means that n could be
* anything in position 1
* -2
* anything in position 2
* 1
or
* anything in position 3.
try writing these cases out if you don't see why.
insufficient, since this list contains numbers that are both inside and outside the range 0 < n < 7.



this means that n could be
* anything in position 3
* 5
* anything in position 4
* 8
or
* anything in position 5.
again, try writing these cases out if you don't see why.
insufficient, since this list contains numbers that are both inside and outside the range 0 < n < 7.

--

together:
looking at the two lists in unison, notice that the only range that's in both lists is position 3. therefore, if we take the two statements together, n must be in position 3.
all the numbers in position 3 fall into the range 0 < n < 7, so this statement is sufficient.

answer (c)