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# The average (arithmetic mean) of x and y

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The average (arithmetic mean) of x and y [#permalink]  19 May 2017, 01:18
Expert's post
00:00

Question Stats:

62% (00:36) correct 37% (00:50) wrong based on 80 sessions

$$x < y$$

 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.
[Reveal] Spoiler: OA

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Director
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Re: x < y [#permalink]  17 Sep 2017, 01:24
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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Re: x < y [#permalink]  18 Sep 2017, 09:49
Expert's post
OE

Quote:
Since x < y, the average of x and y is less than y, so having another y raises the average. Quantity B is greater. ** Plug in the numbers: say x = 2 and y = 4. Quantity A: the average of 2 and 4 is 3. Quantity B: the average of 2, 4, and 4 is 10 + 3 = 3.333, which is more than 3; the second 4 raised the average.

Hope this helps

Regards
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Re: x < y [#permalink]  18 Sep 2017, 14:19
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Expert's post
Carcass wrote:

x < y

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

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.

[Reveal] Spoiler:
B

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Re: x < y [#permalink]  18 Sep 2017, 18:53
Expert's post
Thank you.

Regards
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Re: x < y [#permalink]  21 Sep 2017, 07:04
Now it's clear! Thank you to both of you!
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Re: x < y [#permalink]  26 Oct 2017, 21:30
Hey guys, I don't get how is B either. If you plug in negative values, A becomes larger. Please explain.
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Re: x < y [#permalink]  26 Oct 2017, 23:35
ezinne5189@gmail.com wrote:
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.

Hope it's clear.
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Re: x < y [#permalink]  29 Sep 2018, 10:07
No matter what value one puts the answer will always be B
Re: x < y   [#permalink] 29 Sep 2018, 10:07
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