Data Sufficiency

If the mean of set S is 20, what is the median of set S ?

1. In set S there are as many numbers larger than 20 as there are numbers smaller than 20.
2. All numbers in set S are even integers.

Statement 1: In set S there are as many numbers larger than 20 as there are numbers smaller than 20.

This answer choice is tricky. It seems to point to 20 being the median. However, we can use as an example any set that matches the parameters of both the question and this answer choice. We can also make the examples fit Statement 2, if possible, by using all even numbers.

First lets make the median 20.

Example 1: (10, 20, 30)

Mean: 20 Median: 20

Now let's seek to shift the numbers so that the mean is 20, but the median, which is halfway between the two middle values is not 20. We can do this by using four numbers and placing the inner two and outer two to create a mean of 20, while the mean of the middle two, i.e. the median, is not 20. To get a mean of 20, we just need four numbers that add up to 80. We can move them around many ways, seeking to generate at least two different medians.

Example 2: (0, 10, 30, 40)

Mean: 20 Median: (10 + 30)/2 = 20

Example 3: (0, 0, 30, 50)

Mean: 20 Median: (30 + 0)/2 = 15

Two different medians.

Insufficient.

Statement 2: All numbers in set S are even integers.

We already used this parameter in all examples used for Statement 1.

Insufficient.

Statements Combined:

We combined the statements when creating examples for Statement 1.

Insufficient.

The correct answer is E.