Bunuel wrote:
For a certain set of n numbers, where n > 2, is the average (arithmetic mean) equal to the median?
(1) The n numbers are positive, consecutive even integers.
(2) The average of the n numbers is equal to the average of the largest and smallest numbers in the set.
Kudos for a correct solution.
Target question: Is the average (arithmetic mean) EQUAL to the median? Statement 1: The n numbers are positive, consecutive even integers. There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}
Statement 1 tells us that the numbers are consecutive even integers, which means they are
equally spaced.
As such, we can be certain that
the mean and median are equal.Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average of the n numbers is equal to the average of the largest and smallest numbers in the set. This statement doesn't FEEL sufficient, so I'm going to try testing some different values.
There are several different sets that satisfy this condition. Here are two:
Case a: the numbers are {1, 2, 3}. Here, the mean is equal to the average of the biggest and smallest numbers. In this case
the median and mean ARE equalCase b: the numbers are {-3, -3, 1, 2, 3}. Here, the mean is equal to the average of the biggest and smallest numbers. In this case
the median and mean are NOT equalSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Answer: A
Cheers,
Brent
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