satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X
1) 7<X<11
2) X is the median of five numbers
first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem
I am not convinced with the above answers...
from 1 ) 7 < X< 11 === > X is like 7.1, or 7.2 or 7.5 or 8,8.1 or 9 0r 9.5 ...
there are so many possibilites so i can not take only 8,9,10 as X
so i can not decide from 1
from 2) X is the median of five numbers then === > X, 7,2,16,11 ....
==> how can i arrange if i dont know the value of X in either descending or ascending..
so from the both also it wont be possible to get the ans i believe...
So ans E ...
Do let me know if i am wrong....
There is one more thing we know from the stem: "the average arithmetic mean of the five numbers x, 7, 2, 16, 11 is equal to the median of five numbers" --> \(\frac{x+2+7+11+16}{5}=median\). As there are odd number of terms then the median is the middle term when arranged in ascending (or descending) order but we don't know which one (median could be x, 7 or 11).
, 11, 16 --> \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.
(2) x is the median of five numbers --> the same info as above: \(\frac{x+2+7+11+16}{5}=median=x\) --> \(\frac{x+36}{5}=x\) --> \(x=9\). Sufficient.
Answer: D.