Arithmetic Mean - Problem 104 in Quantitative Review

[scorpion_phoenix]

If x+y=8z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

(A) 2z+1

(B) 3z

(C) 5z

(D) z/3

(E) 3z/2


OA=B


***Having trouble wrapping my head around this one. A thorough explanation would be greatly appreciated.

[Vemuri]

What is the arithmetic mean of x,y&z? Its (x+y+z)/3. Now, its given that x+y=8z. So, when you include this in our original expression ==> (8z+z)/3 ==> 9z/3 ==> 3z (which is the answer).

Hope this helps.

[Jeff@TargetTestPrep]

If x+y=8z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

(A) 2z+1

(B) 3z

(C) 5z

(D) z/3

(E) 3z/2

We need to determine the average of x, y, and z. In other words:

(x + y + z)/3 = ?

Since x + y = 8z, we can substitute 8z for x + y in our average formula and we have:

(8z + z)/3 = 9z/3 = 3z

Answer: B

[Brent@GMATPrepNow]

If x+y=8z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

(A) 2z+1
(B) 3z
(C) 5z
(D) z/3
(E) 3z/2

Jeff has provided an algebraic approach.
Here's a solution that involves the INPUT-OUTPUT approach.

Given: x + y = 8z
So, one possible solution to this equation is x = 7, y = 9 and z = 2

Which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
Average = (x + y + z)/2
= (7 + 9 + 2)/2
= 18/3
= 6

So, when we INPUT x = 2, the answer to the question is 6
So, we're looking for an answer choice that OUTPUTS a 6 when we INPUT x = 2
Let's check the answer choices...

(A) 2(2) + 1 = 5. No good. We want 6. ELIMINATE
(B) 3(2) = 6. KEEP
(C) 5(2) = 10. No good. We want 6. ELIMINATE
(D) 2/3 = 2/3. No good. We want 6. ELIMINATE
(E) 3(2)/2 = 3. No good. We want 6. ELIMINATE

Answer: B

Cheers,
Brent

[Brent@GMATPrepNow]

Jeff and I have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, you can watch the following video:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933

Afterwards, here are some more questions to practice with:
- https://www.beatthegmat.com/what-mistake ... 76293.html
- https://www.beatthegmat.com/car-dealer-s ... 74136.html
- https://www.beatthegmat.com/ps-rate-times-t276107.html
- https://www.beatthegmat.com/to-find-the- ... 73338.html
- https://www.beatthegmat.com/y-dollars-fr ... 73031.html
- https://www.beatthegmat.com/meters-in-x- ... 73854.html
- https://www.beatthegmat.com/a-better-exp ... 79396.html


Cheers,
Brent