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x < y

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x < y [#permalink] New post 01 Jan 2017, 13:16
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Question Stats:

47% (00:21) correct 52% (00:10) wrong based on 21 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)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.


[Reveal] Spoiler:
I found this question in Barrons practice test however, I think the answer is not correct.

My solution:
Since x < y; lets consider two cases. (1) y=4, x= 2 (2) y=-2 x=-5

If we consider the positive case, quantity A is greater. however, If we consider the negative case, quantity B is greater. So the answer should be D.
But the official answer is B. Im not able to understand why!

Any comments?

Thanks!
[Reveal] Spoiler: OA
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Re: x < y [#permalink] New post 01 Jan 2017, 13:58
Thanks for commenting!
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Re: x < y [#permalink] New post 01 Jan 2017, 14:50
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Expert's post
HarveyKlaus wrote:
I found this question in Barrons practise test however, I think the answer is not correct.

My solution:
Since x < y; lets consider two cases. (1) y=4, x= 2 (2) y=-2 x=-5

If we consider the positive case, quantity A is greater. however, If we consider the negative case, quantity B is greater. So the answer should be D.
But the official answer is B. Im not able to understand why!

Any comments?

Thanks!


No, the answer is not D. The answer is B.

In both of your cases, quantity B is greater.

case 1) y=4, x= 2
Quantity A: (4+2)/2 = 3
Quantity B: (4+4+2)/3 = 3 1/3
Quantity B is greater

case 2) y=-2 x=-5
Quantity A: (-2 + -5)/2 = -3.5
Quantity B: (-2 + -2 + -5)/3 = -3
Quantity B is greater

Cheers,
Brent
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5 KUDOS received
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Re: x < y [#permalink] New post 01 Jan 2017, 14:54
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Expert's post
GIVEN: x < y
Quantity A: The average (arithmetic mean) of x and y
Quantity B: The average (arithmetic mean) of x, y and y


Apply the formula for finding the average:
Quantity A: (x + y)/2
Quantity B: (x + y + y)/3

Multiply both quantities by 6 to get:
Quantity A: 3(x + y)
Quantity B: 2(x + y + y)

Expand and simplify 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, the correct answer is B

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Re: x < y [#permalink] New post 26 Sep 2018, 08:17
But can't y be 0?
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Re: x < y [#permalink] New post 15 Oct 2018, 08:23
Hi
I got the approach that Brent sir explained but when I inserted values I got D as ans..
I took x as 2 n y as 3 in that case mean of quantity a is 2.5 n quantity b is 2.6 so B is greater..but if I take x as -3 and y as -2 the mean of quantity a is -2.5 and that of quantity b is -2.6 in which case A is greater..
Please explain me is this wrong to think like this?

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Re: x < y   [#permalink] 15 Oct 2018, 08:23
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