Data Sufficiency

For me, this was tough to solve under two minutes. The explanation in the OG is a bunch convoluted algebraic garbage that's over my head. Hopefully someone can dumb it down for me.

For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?

(1) If no numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.

(2) The range of the n numbers in the set is 2(n-1)

It must A i guess

n = no. of elements in a set
is Mean=Median?

1. If the difference b/w any pair of successive numbers is 2, then Mean must be equal to Median.

In fact, There is a very important point to note here. It is true for any set which has equally spaced elements(Whatever the difference is) ==> Mean will be equal to Median.

Let's try it out.
Set = {1,2,3,4}, Mean = (1+2+3+4)/4 = 2.5 = Median = (2+3)/2 [Difference of any successive element is 1]
Set = {1,3,5,7}, Mean = (1+3+5+7)/4 = 4 = Median = (3+5)/2 [Difference of any successive element is 2]
Set = {1,4,7,10,13}, Mean = (1+4+7+10+13)/5 = 7 = Median = 7 [Difference of any successive element is 3]

So, it's clearly sufficient.

2. Range of the n numbers = 2(n-1)

Set = {1,2,7}, n=3, Range = 7-1 = 6 [Mean is NOT equal to Median. NO]
Set = {2,4,6,8}, n=3, Range = 8-2 = 6 [Mean is equal to Median. YES]

Insufficient.

You get 2 answers

Papgust,

can you please explain the "2(n-1)"? The reason I am asking is because in both your examples, you have used n=3 but there are 3 numbers in the first and 4 in the second.

Thanks,

EMAN wrote:For me, this was tough to solve under two minutes. The explanation in the OG is a bunch convoluted algebraic garbage that's over my head. Hopefully someone can dumb it down for me.

For a certain set of n numbers, where n>1, is the average (arithmetic mean) equal to the median?

(1) If no numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.

(2) The range of the n numbers in the set is 2(n-1)

Statement 1:
When a set of numbers is EVENLY SPACED, the average = the median.
SUFFICIENT.

Statement 2:
If n=3 -- implying a set of 3 numbers -- then the range = 2(3-1) = 4.

Test one case that also satisfies statement 1, which requires a distance of 2 between successive numbers:
{1, 3, 5}
Here, because the numbers are EVENLY SPACED, the average = the median.

Test one case that DOESN'T satisfy statement 1:
[1, 1, 5]
Here, the average = (1+1+5)/3 = 7/3, while the median = 1.

Since the average is equal to the median in the first case but not in the second case, INSUFFICIENT.

The correct answer is A.

In an arithmetic sequence (a sequence of numbers that are evenly spaced), average is always equal to median. The solution below is taken from the GMATFix App.



-Patrick

Patrick,

Thank you very much for posting the video, however, in my opinion, I would recommend using numerical examples when explaining the Arithmetic sequence.

Thank you very much.

Patrick_GMATFix wrote:In an arithmetic sequence (a sequence of numbers that are evenly spaced), average is always equal to median. The solution below is taken from the GMATFix App.



-Patrick

Thanks for the tip. I thought that using numbers to explain would just show an example rather than explain the logic behind the property I explain in the video, but maybe you're right.

Thanks for the feedback! I'm glad you found the video helpful.

-Patrick