What is the average (arithmetic mean) of eleven consecutive integers?

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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.

Answer: D

Source: GMAT Prep

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M7MBA wrote:
Fri May 14, 2021 2:06 am
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.

Answer: D

Source: GMAT Prep
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
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