We can solve the question using matching operations

First apply the formula for finding averages
Quantity A: (x + y)/2
Quantity B: (x + y + y)/3

Simplify Quantity B to get:
Quantity A: (x + y)/2
Quantity B: (x + 2y)/3

Eliminate that fractions by multiplying both quantities by 6 (the least common multiple of 2 and 3)
When we do this, we get:
Quantity A: 3(x + y)
Quantity B: 2(x + 2y)

Expand to get:
Quantity A: 3x + 3y
Quantity B: 2x + 4y

Subtract 2x from both quantities to get:
Quantity A: x + 3y
Quantity B: 4y

Subtract 3y from both quantities to get:
Quantity A: x
Quantity B: y

Since we're told that x < y, we can conclude that Quantity B is greater.

Answer:

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How could the answer be B? Without any restriction about the values of x and y, they could also be both equal to zero and then A and B would be equal. Otherwise, if for example x = 1 and y = 2, then column A would be 3/2, while column B would be 5/2, thus column B would be greater. Since there is no unique relationship, the answer should be D!

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Hope this helps

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Thank you.

Regards
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Now it's clear! Thank you to both of you!

Hey guys, I don't get how is B either. If you plug in negative values, A becomes larger. Please explain.

x < y

Quantity A	Quantity B
The average (arithmetic mean) of x and y	The average (arithmetic mean) of x, y and y

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

SOLUTION:

The average (arithmetic mean) of x and y is (x + y)/2

The average (arithmetic mean) of x, y and is (x + y + y)/3

(x + y)/2 ? (x + y + y)/3

3x + 3y ? 2x + 4y

x ? y

Since we are given in the stem that x < y, then ? is < sign, which means that Quantity B is greater.

Answer: B.

Hope it's clear.

No matter what value one puts the answer will always be B

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