What is the average of n x , n y, n z, and n w?

Target question: What is the average of n − x , n − y, n − z, and n − w?

In other words, we want to find the value of \(\frac{(n-x)+(n-y)+(n-z)+(n-w)}{4}\)

This expression can also be expressed as follows: \(\frac{4n-x-y-z-w}{4}\)

Even better we can rewrite it like this: \(\frac{4n- (x+y+z+w)}{4}\)

Statement 1: The average of x, y, z and w is 4n.
This statement is telling us that \(\frac{x+y+z+w}{4}=4n\)

Multiply both sides of the equation by \(4\) to get: \(x+y+z+w=16n\)

We can now substitute this value into our target expression to get: Average = \(\frac{4n- (x+y+z+w)}{4}=\frac{4n- (16n)}{4}=\frac{-12n}{4}=-3n\)

Since we don't know the value of n, there's no way to enter the target question with certainty
Statement 1 is NOT SUFFICIENT


Statement 2: \(n = 120\)
Since we have no information about the values of x, y, z and w, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the average of the four numbers is \(-3n\)
Statement 2 tells us that \(n = 120\)
So, we now know that the average of the four numbers \(= -3n = -3(120) = -360\)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent