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What is the value of x^3 - y^3 ?

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What is the value of x^3 - y^3 ? [#permalink] New post 10 Oct 2010, 02:46
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57% (01:52) correct 43% (00:17) wrong based on 30 sessions
What is the value of x^3 - y^3 ?

(1) x^6 - y^6 = 0
(2) y = 0
[Reveal] Spoiler: OA
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Re: Powers doubt [#permalink] New post 10 Oct 2010, 02:54
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vivaslluis wrote:
Hi,

I have a doubt with the following question:
- What is the value of x^3 - y^3 ?
(1) x^6 - y^6 = 0
(2) y = 0

I discard A, B and D because there's not enough information. I know the answer is C, but I don't get a clue of why.

Could someone help me with that?

Thank you!


x^6-y^6=0 and y=0
So x^6-0^6=0
So x=0
So x^3-y^3=0
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Re: Powers doubt [#permalink] New post 10 Oct 2010, 10:12
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vivaslluis wrote:
Hi,

I have a doubt with the following question: - What is the value of x^3 - y^3 ?
(1) x^6 - y^6 = 0
(2) y = 0

I discard A, B and D because there's not enough information. I know the answer is C, but I don't get a clue of why.

Could someone help me with that?

Thank you!


So you need x^3 - y^3.

Statement 1:

x^6 - y^6 = (x^3 - y^3)(x^3+y^3) = 0

Insufficient, since either one of the two terms could be zero.

Statement 2:

y^3 = 0, which means x^3 - y^3 = x^3. Still insufficient.

Combining both, and substituting y = 0 in the second statement, we get : x^6 = 0, which means x = 0, and hence x^3 - y^3 = 0

Hence the answer is C.
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Re: Powers doubt [#permalink] New post 10 Oct 2010, 13:47
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Crystal clear. Thank you! :-D
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Re: Powers doubt [#permalink] New post 23 Dec 2010, 08:06
I disagree with explanations given above. Here is my approach:

Stmt (1) indicates that x=y otherwise x^6-y^6=0 does not hold true. Hence, x^3-y^3 is always equal to zero. SUFF.

Stmt (2) is clearly INSUFF because there is no inf. about x.

If my approach is wrong, I would appreciate any other explanations.
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Re: Powers doubt [#permalink] New post 23 Dec 2010, 08:30
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feruz77 wrote:
I disagree with explanations given above. Here is my approach:

Stmt (1) indicates that x=y otherwise x^6-y^6=0 does not hold true. Hence, x^3-y^3 is always equal to zero. SUFF.

Stmt (2) is clearly INSUFF because there is no inf. about x.

If my approach is wrong, I would appreciate any other explanations.


Yes, your approach is wrong: x^6-y^6=0 implies that either x=y or x=-y, for example 1^6-1^6=0 and also 1^6-(-1)^6=0. To see this algebraically you could rewrite x^6-y^6=0 as (x^3-y^3)(x^3+y^3)=0 --> either x^3=y^3, or x^3=-y^3 --> so either x=y or x=-y. OR x^6-y^6=0 --> x^6=y^6 --> x^2=y^2 --> x=y or x=-y.

Now, if x=y then x^3-y^3=0 for any values of x and y BUT of x=-y then x^3-y^3=2x^3 and we need the value of x (or y) the get the single numerical value of 2x^3. So statement (1) is not sufficient.

(2) y=0 --> clearly insufficient.

(1)+(2) y=0, so x=0 too (as x^6-y^6=0) and x^3-y^3=0. Sufficient.

Answer: C.

Hope it's clear.
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Re: Powers doubt [#permalink] New post 24 Dec 2010, 03:46
This is not tough question, but you need to be carefull not to fall into trap of ODD POWER of numbers. you always need to be suspicious when you see one.
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Re: Powers doubt   [#permalink] 24 Dec 2010, 03:46
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