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Source: Beat The GMAT — Data Sufficiency |
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akshatsingh
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codesnooker
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LOL anybody can just say both are sufficient as answer is given. Please help others.akshatsingh wrote:Easily, both are suficent
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.