Data Sufficiency

Olga Lapina wrote:What is the average (arithmetic mean) of eleven consecutive integers?

1. The average of the first 9 integers is 7
2. The average of the last 9 integers is 9

Hi Olga,

Actually, the correct answer is D. You may want to recheck the answer key.


Target question: What is the average (arithmetic mean) of 11 consecutive integers?

Statement 1: The average of first nine integers is 7
IMPORTANT: There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For more on this concept, see https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean

We can apply this rule to this question, since consecutive integers are equally spaced.
So, if the mean of the first nine integers is 7, then the median of the first nine integers is 7.
So, the first nine integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The average of last nine integers is 9
If the mean of the last nine integers is 9, then the median of the last nine integers is 9.
So, the last nine integers must be 5, 6, 7, 8, 9, 10, 11, 12, 13
This means the 11 numbers are 3,4,5,6,7,8,9,10,11,12,13
Since the median of this set is 8, the mean must be 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent