Brent@GMATPrepNow wrote:Here's a 700-level question I just made up:

The average (arithmetic mean) of y numbers is x. If z is added to the numbers, the new average (arithmetic mean) will be z-5. What is the value of z in terms of x and y?

A) x + 5/y + 5

B) (xy + 5y)/(y - 1)

C) (xy - 5)/(y+1)

D) x/(y+1) - 5y

E) x - 5/y

Let z=5, implying that -- after 5 is added to the original numbers -- the resulting average = z-5 = 5-5 = 0.

For the resulting average to be 0, the sum after 5 is added must also be equal to 0.
Implication:
The sum of the original numbers must be -5.
Let y=1 and x=-5, with the result that the sum of the original numbers = (number of numbers)(average of the numbers) = (1)(-5) = -5.

The question stem asks for the value of z=5. This is our target.
Now plug y=1 and x=-5 into the answer choices to see which yields our target of 5.
Only A works:
x + 5/y + 5 = -5 + 5/1 + 5 = 5.

The correct answer is A.

Brent@GMATPrepNow wrote:Here's a 700-level question I just made up:

The average (arithmetic mean) of y numbers is x. If z is added to the numbers, the new average (arithmetic mean) will be z-5. What is the value of z in terms of x and y?

A) x + 5/y + 5

B) (xy + 5y)/(y - 1)

C) (xy - 5)/(y+1)

D) x/(y+1) - 5y

E) x - 5/y

Answer: A

Brent original!

We can also do a little algebra here. Initially, the sum = average * number = x * y.
If we add 'z' our new sum will be xy + z. And if we initially had y numbers, we'll have y + 1 numbers after adding one more.

To summarize
new sum = xy + z
new number of terms = y + 1
New average = (xy + z)/(y +1)

We're told this new average is equal to z - 5. So (xy + z)/(y +1) = z - 5 ---> xy + z = (z-5)(y+1) ---> xy + z = zy - 5y + z - 5 ---> xy + 5y + 5 = zy
x + 5 + 5/y = z; The answer is A