Easily, both are suficent

care to explain? Thanks

akshatsingh wrote:Easily, both are suficent

LOL anybody can just say both are sufficient as answer is given. Please help others.

Anyway, I will try to explain the answer:-

Our data set is {7, 2, 16, 11, x}

Now rearrange the data set in the ascending order. Forget the placement of the x as we don't know its value.

data set = {2, 7, 11, 16 and x (without placement for the moment)}

Arithmetic Mean = AM = (2 + 7 + 11 + 16 + x)/5
AM = (36 + x) / 5
Now according to the question, its given that AM = Median (M).
i.e. AM = M

Now median is the value from the dataset which come in the middle of the dataset.

Now According to first statement:

7 < x < 11 (it means x lies between 7 and 11 in the data set.)

Therefore Median = M = x

as M = AM = (36 + x)/5

therefore, x = (36 + x)/5
i.e. x = 9

SUFFICIENT

Now lets take the second statement:
x is the median of the numbers:
i.e. same as we have proved in statement 1. Hence again x = 9

SUFFICIENT

Therefore (D) is the answer.

PS: I will suggest you to study Mean, Mode, Median and Standard Deviation first and solve some problems.

Thank you! Tough to see but when you line up the numbers in ascending order it comes a bit clearer.

Thank you for your time in writing it out. Much appreciated.