brbanks1 wrote:
Set K consists of a finite number of consecutive odd integers. If x is the smallest number in K and y is the greatest, then y - x =
(1) The average (arithmetic mean) of set K is -36.
(2) There are 8 numbers in set K.
Target question: What is the value of y - x?
Given: Set K consists of a finite number of consecutive odd integers
Statement 1: The average (arithmetic mean) of set K is -36
There's a nice rule that says,
"In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}
Set K consists of consecutive odd integers, so the values are EQUALLY SPACED.
Since the mean of set K is -36, we know that the MEDIAN is -36 as well.
HOWEVER, we don't know the number of elements in set K.
So, consider these two possible sets that yield conflicting answers to the
target question:
Case a: set K = {-37, -35}, so the average is -36. In this case
y - x = -35 - (-37) = 2
Case b: set K = {-39, -37, -35, -33}, so the average is -36. In this case
y - x = -33 - (-39) = 6
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There are 8 numbers in set K.
We already know that the numbers are consecutive ODD integers.
This means that each number in the set is 2 GREATER than the one before it.
So, if we let
x = the
smallest (1st) value in set K
Then x + 2 = the 2nd value in set K
And x + 4 = the 3rd value in set K
And x + 6 = the 4th value in set K
And x + 8 = the 5th value in set K
And x + 10 = the 6th value in set K
And x + 12 = the 7th value in set K
And
x + 14 = the 8th value in set K
In other words,
x + 14 = y, the
largest value in set K
So,
y - x = (x + 14) - x = 14
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
