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Carcass
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xy<0 [#permalink] New post   30 Mar 2022, 02:00
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Question Stats:

41% (00:43) correct 58% (00:35) wrong based on 12 sessions

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\(xy<0\)

Quantity A
Quantity B
\([x+y]^2\)
\( [x-y]^2\)



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


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B
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GreenlightTestPrep
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xy<0 [#permalink] New post   30 Mar 2022, 05:51
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Carcass wrote:
\(xy<0\)

Quantity A
Quantity B
\([x+y]^2\)
\( [x-y]^2\)



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



We can solve this question using matching operations (see the video lesson below )

Given:
Quantity A: (x + y)²
Quantity B: (x - y)²

Expand and simplify both quantities:
Quantity A: x² + 2xy + y²
Quantity B: x² - 2xy + y²

Subtract x² and subtract y² from both quantities:
Quantity A: 2xy
Quantity B: -2xy

Add 2xy to both quantities:
Quantity A: 4xy
Quantity B: 0

Since we're told xy is negative, we know that 4xy is negative, which means Quantity B is greater.

Answer: B

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rx10
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Re: xy<0 [#permalink] New post   30 Mar 2022, 03:00
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\(xy<0\)

Qt A :: \((x+y)^2\) \(= x^2 + y^2 + 2xy\)

Qt B :: \((x-y)^2\) \(= x^2 + y^2 - 2xy\)

Since \(xy < 0\)

Qt B > Qt A

Answer B
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gmatclubot
Re: xy<0 [#permalink]
30 Mar 2022, 03:00
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