Set K consists of a finite number of consecutive odd

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

D'oh!

I keep falling into these traps. Hopefully, practice will allow me to master them eventually...

What about this set: (-5,-3,-1,1,3,5,7). Y-X = 12 in this case.

There are 7 numbers in your set, not 8.

Bunuel, Could you please help to explain or elaborate the statement as highlighted in red? y=x+2(n-1)

Source : Magoosh

It's the formula of nth term of arithmetic progression. Check here: https://gmatclub.com/forum/math-sequenc ... 01891.html

Statement 1= tells us there are even number of turns and middle two terms are -35 and -37. But there can be possibly infinite such sequences.
For Example- {-37,-35}, {-39,-37,-35.-33} and so on
y-x can have infinite values

Statement 2 - There are 8 terms
y=x+(k-1)2
y-x=7*2=14
Sufficient

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.
(x +y) = -36*2. or, x + x +2(n-1) =-36*2 or, 2x +2(n-1) = -72 Not Sufficient.

(2) There are 8 numbers in set K.
y = x +2(n-1) or, y-x = 2(n-1) = 2*7 =14. Sufficient

So, It is B.