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# x2 + y2 = 81 x2 - y2 = 0

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Founder
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x2 + y2 = 81 x2 - y2 = 0 [#permalink]  12 Aug 2019, 02:05
Expert's post
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Question Stats:

83% (00:44) correct 16% (00:12) wrong based on 6 sessions
$$x^2 + y^2 = 81$$

$$x^2 - y^2 = 0$$

 Quantity A Quantity B $$x^4-y^4$$ $$0$$

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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GRE Instructor
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Kudos [?]: 2208 [1] , given: 27

Re: x2 + y2 = 81 x2 - y2 = 0 [#permalink]  12 Aug 2019, 09:11
1
KUDOS
Expert's post
Carcass wrote:
$$x^2 + y^2 = 81$$

$$x^2 - y^2 = 0$$

 Quantity A Quantity B $$x^4-y^4$$ $$0$$

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.

Nice question!
I like it because we can ignore the first equation, and just use the second equation.

Take: $$x^2 - y^2 = 0$$
Add $$y^2$$ to both sides to get: $$x^2 = y^2$$
Square both sides to get: $$(x^2)^2 = (y^2)^2$$
Simplify by applying the Power of a Power law to get: $$x^4 = y^4$$
Rewrite as follows: $$x^4 - y^4 = 0$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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Intern
Joined: 15 Aug 2019
Posts: 31
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Kudos [?]: 20 [1] , given: 3

Re: x2 + y2 = 81 x2 - y2 = 0 [#permalink]  17 Aug 2019, 02:15
1
KUDOS
# (A+B) * (A-B) = A^2 - B^2
So (x^2+y^2) * (x^2-y^2) = (x^4-y^4)
=> 81 * 0 => 0
Ans is C.
Re: x2 + y2 = 81 x2 - y2 = 0   [#permalink] 17 Aug 2019, 02:15
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# x2 + y2 = 81 x2 - y2 = 0

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