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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The average (arithmetic mean) of x and z is greater than y,  Question banks Downloads My Bookmarks Reviews Important topics
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The average (arithmetic mean) of x and z is greater than y, [#permalink]
Expert's post 00:00

Question Stats: 75% (00:22) correct 25% (00:59) wrong based on 20 sessions
The average (arithmetic mean) of x and z is greater than y, and $$x < y < z$$.

 Quantity A Quantity B The average of x, y, and z The median of x, y, and z

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

Kudos for the right answer and solution.
[Reveal] Spoiler: OA

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GRE Instructor Joined: 10 Apr 2015
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Re: The average (arithmetic mean) of x and z is greater than y, [#permalink]
Expert's post
Carcass wrote:
The average (arithmetic mean) of x and z is greater than y, and $$x < y < z$$.

 Quantity A Quantity B The average of x, y, and z The median of x, y, and z

Since $$x < y < z$$, we can see that the median of the set must be y. So Quantity B = y

We have:
Quantity A: $$\frac{x + y + z}{3}$$

Quantity B: $$y$$

Multiply both quantities by 3 to get:
Quantity A: $$x + y + z$$
Quantity B: $$3y$$

Subtract $$y$$ from both quantities to get
Quantity A: $$x + z$$
Quantity B: $$2y$$

GIVEN: The average (arithmetic mean) of x and z is greater than y

We can write: $$\frac{x + y}{2} > y$$

Multiply both sides of the inequality by 2 to get: $$x + y > 2y$$

Perfect! This last bit of information tells us that Quantity A must be greater

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Brent Hanneson – Creator of greenlighttestprep.com  Re: The average (arithmetic mean) of x and z is greater than y,   [#permalink] 16 Nov 2019, 07:11
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