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# If x^6 – y^6 = 0, what is the value of x^3 – y^3?

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
If x^6 – y^6 = 0, what is the value of x^3 – y^3?  [#permalink]

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22 Oct 2017, 06:53
2
1
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Difficulty:

45% (medium)

Question Stats:

63% (01:42) correct 37% (02:03) wrong based on 49 sessions

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If x^6 – y^6 = 0, what is the value of x^3 – y^3?

(1) x is positive.
(2) y is greater than 1.

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Manager
Joined: 05 Oct 2014
Posts: 56
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: If x^6 – y^6 = 0, what is the value of x^3 – y^3?  [#permalink]

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22 Oct 2017, 07:20
X6 – y6 =0
=> (X3)2 – (y3)2 =0 => (X3 + y3) (X3 - y3) = 0

So,

Either, (X3 + y3) =0 implies x=-y or y=-x

Or, (X3 - y3) = 0 implies x=y

(1) says , x is +ve , but we don’t know the value of y. INSUFFICENT

(2) says y>1 , we don’t know the value of x. INSUFFICEIENT

Adding (1) + (2) , (X3 - y3) must be 0

Answer should be C
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Re: If x^6 – y^6 = 0, what is the value of x^3 – y^3?  [#permalink]

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22 Oct 2017, 07:39
1
x^6 - y^6 = 0 ==>(x^3-y^3)*(x^3+y^3)=0

==>(x^3-y^3)=0 or (x^3+y^3)=0 or both =0

(1)x is positive.-- No Info abt y- Not suff
(2) y is greater than 1. -- No Info abt x- Not suff

Combining (1) and (2) we get: x is positive and y>1,It means both are positive hence (x^3+y^3) >0

Therefore (x^3-y^3) =0

Hence C
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Re: If x^6 – y^6 = 0, what is the value of x^3 – y^3? &nbs [#permalink] 22 Oct 2017, 07:39
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# If x^6 – y^6 = 0, what is the value of x^3 – y^3?

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