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# If x^2 + y^2 = 16 - 2xy, then (x + y)^4 =

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Kudos [?]: 1449 [0], given: 6611

If x^2 + y^2 = 16 - 2xy, then (x + y)^4 = [#permalink]  24 Mar 2018, 05:11
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Question Stats:

100% (00:17) correct 0% (00:00) wrong based on 4 sessions
If $$x^2 + y^2 = 16 - 2xy$$, then $$(x + y)^4 =$$

A. 4

B. 32

C. 48

D. 64

E. 256
[Reveal] Spoiler: OA

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Joined: 15 Jan 2018
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GMAT 1: Q V
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Kudos [?]: 188 [1] , given: 0

Re: If x^2 + y^2 = 16 - 2xy, then (x + y)^4 = [#permalink]  25 Mar 2018, 19:45
1
KUDOS
Key to this one is noticing the hidden special equation. x^2 + y^2 isn't one, but it's close. If you shuffle the equation around a bit you get:

x^2 + 2xy + y^2 = 16

which can be reformatted to:

(x + y)^2 = 16

Since (x + y)^4 is (x + y)^2 squared, we can say that:

(x + y)^4 = 16^2

which is 256, giving us answer choice E.
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Re: If x^2 + y^2 = 16 - 2xy, then (x + y)^4 =   [#permalink] 25 Mar 2018, 19:45
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