Economist 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) = 2Case b: set K = {-39, -37, -35, -33}, so the average is -36. In this case

y - x = -33 - (-39) = 6Since 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 = 14Since we can answer the

target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,

Brent

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