runningguy wrote:If the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers?
1) The range of the n integers is 14.
2) The greatest of the n integers is 17.
Target question: What is the least of the integers?
Statement 1: The range of the n integers is 14.
There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."
Since consecutive odd integers are equally spaced, the mean of the integers will equal the median.
So, we know that the "middlemost" value is 10.
Since 10 is not odd, we now know that there must be an even number of odd integers in the set, and the average of the TWO MIDDLEMOST integers is 10.
If the median is 10, then half of the odd integer are greater than 10, and half are less than 10.
Since the range is 14, we know that the greatest value is 10+7 and the least value is 10-7
So, the integers are
3,5,7,9,11,13,15,17, which means
the smallest value is 3
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The greatest of the n integers is 17
There's another nice rule that says,
In a set where the numbers are equally spaced, the mean = (largest value - smallest value)/2
So, we know that 10 = (17 - smallest value)/2
From this, we can conclude that
the smallest value must be 3
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
D
Cheers,
Brent
