Check out this mean and consecutive numbers question from GMAT Prep!
What is the average (arithmetic mean) of 11 consecutive integers?
1) the average of the first nine integer equals 7
2) the average of the last nune integer equals 9.
To start, recognize that this is a “value” DS question, so we need to know the exact average in order to have sufficiency.
Average = sum of terms/ # of terms
Avg = (a + b + c + d + e + f + g + h + i + j + k) / 11
We know the 11 numbers are consecutive, so we need to know at least one of the numbers and its placement to find the set.
7 = (a + b + c + d + e + f + g + h + i) / 9
63 = a + b + c + d + e + f + g + h + i
What 9 consecutive numbers sum to 63?
Let’s call the middle number x. We can re-write the sequence as:
63 = (x – 4)+(x – 3)+(x – 2)+(x – 1)+(x)+(x + 1)+(x + 2)+(x + 3)+(x + 4)
63 = 9x
7 = x = middle number of the first 9 terms. We can find the other numbers now since we know they are consecutive integers.
The set is 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
The same logic applies. We can determine the set. The answer is (D).