zz0vlb wrote:
What is the average (arithmetic mean) of eleven consecutive integers?
(1) The average of the first nine integers is 7
(2) The average of the last nine integers is 9
There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."Since the consecutive integers are equally-spaced,
their mean and median will be equal.
Target question: What is the average of eleven consecutive integers? 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
Statement 2: The average of the last night integers is 9 This also tells us that the MEDIAN of the last nine integers is
9.
In other words, the MIDDLEMOST value is
9.
This means, the last nine integers are 5, 6, 7, 8,
9, 10, 11, 12, 13
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 2 is SUFFICIENT
Answer: D
RELATED VIDEO
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Students often get questions wrong NOT because they lack the skills to solve the question, but because they don’t understand what the GMAT is testing Learn more