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GRE Math Challenge #32- 4x^2 + 4y^2

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GRE Math Challenge #32- 4x^2 + 4y^2 [#permalink] New post 19 Sep 2014, 02:59
Expert's post
00:00

Question Stats:

72% (00:42) correct 27% (00:14) wrong based on 33 sessions
Column A: 4x^2 + 4y^2
Column B: (2x + 2y)^2

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: OA

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Re: GRE Math Challenge #32 [#permalink] New post 13 Apr 2015, 06:04
Expert's post
sandy wrote:
----------------------------------------------
Column A: 4x² + 4y²
Column B: (2x + 2y)²

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.

---------------------------------------------
Column A: 4x² + 4y²
Column B: (2x + 2y)²

Expand and simplify Column B to get:
Column A: 4x² + 4y²
Column B: 4x² + 8xy + 4y²

Now we'll use the strategy of performing the same operations on both columns

Subtract 4x² and 4y² from both columns to get:
Column A: 0
Column B: 8xy

To make things super clear, let's divide both columns by 8 to get:
Column A: 0
Column B: xy

At this point, we can see that the answer is
[Reveal] Spoiler:
D

To see why, consider these two possible cases:
case #1: x = 0 and y = 1, which means the two columns are equal
case #2: x = 1 and y = 1, which means the two columns are NOT equal

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: GRE Math Challenge #32- 4x^2 + 4y^2 [#permalink] New post 11 Mar 2018, 06:24
sandy wrote:
Column A: 4x^2 + 4y^2
Column B: (2x + 2y)^2

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.


When the stem doesn't specify the value of x and y. It is easier to plug 0 and 1 to weigh the two column.

IF x and y=0

Quant A would be 0= Quant B

IF x and y=1

Quant A = 8

Quant B = 16

Thus ans= D
Re: GRE Math Challenge #32- 4x^2 + 4y^2   [#permalink] 11 Mar 2018, 06:24
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GRE Math Challenge #32- 4x^2 + 4y^2

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