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x < y

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HarveyKlaus

Intern

Joined: 22 Aug 2016

Posts: 33

x < y [#permalink]

01 Jan 2017, 13:16

00:00

Question Stats:

61% (00:27) correct

38% (00:24) wrong

based on 92 sessions

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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.

Show: ::

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!

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GreenlightTestPrep

GRE Instructor

Joined: 10 Apr 2015

Posts: 6038

Re: x < y [#permalink]

01 Jan 2017, 14:54

Expert Reply

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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General Discussion

HarveyKlaus

Intern

Joined: 22 Aug 2016

Posts: 33

Re: x < y [#permalink]

01 Jan 2017, 13:58

Thanks for commenting!

GreenlightTestPrep

GRE Instructor

Joined: 10 Apr 2015

Posts: 6038

Re: x < y [#permalink]

01 Jan 2017, 14:50

Expert Reply

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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mellowtubmarine

Intern

Joined: 26 Sep 2018

Posts: 1

Re: x < y [#permalink]

26 Sep 2018, 08:17

But can't y be 0?

Reetika1990

Intern

Joined: 20 Sep 2018

Posts: 14

Re: x < y [#permalink]

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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