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# MGMAT Challenge: Zenzizenzizenzic Zurprise

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MGMAT Challenge: Zenzizenzizenzic Zurprise [#permalink]  13 Jul 2010, 18:42
X^8 - Y^8 =

A. (X^4 - Y^4)^2
B. (X^4 + Y^4)(X^2 + Y^2)(X + Y)(X - Y)
C. (X^6 + Y^2)(X^2 - Y^6)
D. (X^4 - Y^4)(X^2 - Y^2)(X - Y)(X + Y)
E. (X^2 - Y^2)^4

OA:
[Reveal] Spoiler:
B

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Re: MGMAT Challenge Problem [#permalink]  13 Jul 2010, 19:39
1
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Apply a^2 - b^2 = (a-b)(a+b)

(x^4)^2 - (y^4)^2

( x^4 + y^4) ( x^4 - y^4)

( x^4 + y^4) (x^2+y^2)(x^2-y^2)

( x^4 + y^4) (x^2+y^2)(x+y)(x-y)

So B
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Re: MGMAT Challenge Problem [#permalink]  14 Jul 2010, 05:44
Looks like 500-level question))
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Re: MGMAT Challenge Problem [#permalink]  14 Jul 2010, 06:13
1
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The solution is just a basic application of the principle that x^2 - y^2 = (x+y)(x-y)

So, when we simplify, we treat x^8 = (x^4)^2 = ((x^2)^2)^2

So we get the following:

x^8 - y^8 = (x^4+y^4)(x^4-y^4) = (x^4+y^4)(x^2+y^2)(x^2 - y^2) =(x^4+y^4)(x^2+y^2)(x+y)(x-y)

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Re: MGMAT Challenge Problem [#permalink]  14 Jul 2010, 06:56
ulm wrote:
Looks like 500-level question))

Agreed. I personally think that it belongs in the 600-level category, but MGMAT considers it a 700-level question. I just wanted to stay as faithful to the question source as possible.

I'll post a harder one to make up for it!
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Re: MGMAT Challenge Problem [#permalink]  16 Jul 2010, 00:24
I go with option B

It is definitely not a 700 level problem
Re: MGMAT Challenge Problem   [#permalink] 16 Jul 2010, 00:24
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