Lesson: When Mean = Median

Comment on When Mean = Median

Brent, would that be a true statement that if the numbers in a set are evenly spaced, then there is a fast way to calculate the Mean: (Smallest number+Largest Number)/2. WDYT?
gmat-admin's picture

That is 100% true!

Hi Brent,

In the below question, when I tried solving it my answer was D, the random values that I took answered the question with certainty but when I look at the solutions of others I noticed they used the same approach but with different values and hence got the answer E, which is the current answer. My issue is that is trial and error the only way of handling such questions, if yes and any strategy to choose values?

gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-is-an-integer-is-the-median-of-the-5-num...

You've just described the biggest flaw with the strategy of testing values.
If, by testing values, you are able to get two DIFFERENT answers to the target question, then the statement is NOT sufficient.

However, if you are NOT able to get two DIFFERENT answers to the target question, then it may be the case that the statement is sufficient OR it may be the case that you haven't tested the right values.

To learn more about the limitations of testing values, read http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values


Hi Brent,

I have a doubt from your solution regarding this question below.

"Statement 1: The average of the first nine integers is 7.
This also tells us that the MEDIAN of the first nine integers is 7.
In other words, the MIDDLEMOST value is 7.
This means, the first nine integers are 3, 4, 5, 6, 7, 8, 9, 10, 11
So, ALL 11 integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Since we've identified all 11 integers, we can DEFINITELY find their average.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT"

How do we know that "equally spaced" is 1, why not 2 or 2 or else?

gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-average-arithmetic-mean-of-eleven...

In this question, we're told that there are "eleven CONSECUTIVE integers?"

"CONSECUTIVE integers" always refers to a set of numbers in which each number is 1 greater than the previous number.

If the question had read "11 CONSECUTIVE EVEN integers," then each number would be 2 greater than the previous number.


oh thank you. That meant if we were not told "eleven consecutive integers", we cannot conclude that number is 1 greater than the previous number?
gmat-admin's picture

That's correct.

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