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If abc is not equal to 0, what is the value of (a^3 + b^3 + [#permalink]
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16 Jul 2003, 02:16
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This topic is locked. If you want to discuss this question please repost it in the respective forum. If abc is not equal to 0, what is the value of (a^3 + b^3 + c^3)/(abc)?
(1). a=1, b=2, c=3
(2). a + b + c = 0
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
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AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



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Joined: 03 Feb 2003
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all the numbers are nonzero ones.
(1) is obviously not enough
consider a=1, b=2, c=3 and a=1, b=2, c=3
(2) of no use alone
consider
a=10, b=9, c=1
a=1, b=1, c=2
combine: the only possible combination for a+b+c=0 is a=1, b=2, c=3
Thus, I vote for C.



Intern
Joined: 06 Jul 2003
Posts: 3

The answer is C.
1 alone is not enough. 2 alone is not enough, either.
1 and 2 taken together are possible only when
a) a=1, b=2, c=3 or
b) a=1, b=2, c=3
but the results in both cases are the same
a) (1+827)/6
b) (18+27)/6 = (1+827)/6



Manager
Joined: 07 Jul 2003
Posts: 56

terrific!
I'd vote for E. Cuz really there are two different solutions when we consider C. But I never calculate till end!!!



Manager
Joined: 08 Apr 2003
Posts: 150

C for me too...
Spilt up the equation to this form,
b^2+c^2/bc + a^2+c^2/ac + a^2+b^2/ab +6.



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Any more tries?
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AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



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try 1, 2, 3 = (1+8+27)/6=36/6=6
try 1, 2,3 = (1+827)/(6)=18/6=3
clearly (1) is not sufficient



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stolyar wrote: try 1, 2, 3 = (1+8+27)/6=36/6=6 try 1, 2,3 = (1+827)/(6)=18/6=3
clearly (1) is not sufficient
Can't challenge a counterexample. Okay, we eliminate A and D. What now?
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AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



SVP
Joined: 03 Feb 2003
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It is B, unfortunately.
But why?



Manager
Joined: 08 Apr 2003
Posts: 150

OKies got my mistake while working through it.
I just thought on reducing the values A^3+b^3+C^3 and the following formula striked me.
a^3 + b^3 + c^3 = (a+b+c)(a^2abacbc+b^2+c^2) + 3abc
So Considering that if we use B, we have the answer as 3.
Hope that's right..



Manager
Joined: 08 Apr 2003
Posts: 150

I guess if such type of problem appaear on GMAT, all what is required is nice clean trick striking at the correct moment othwerwise, one would land up wasting 4 to 5 minutes solving it for actual.



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evensflow wrote: OKies got my mistake while working through it. I just thought on reducing the values A^3+b^3+C^3 and the following formula striked me. a^3 + b^3 + c^3 = (a+b+c)(a^2abacbc+b^2+c^2) + 3abc So Considering that if we use B, we have the answer as 3. Hope that's right..
What is the formula that you use for a sum of cubes?



Manager
Joined: 08 Apr 2003
Posts: 150

My idea behind the thought was...
a^3 + b^3 = (a + b)(a^2 ab + b^2)
Work on the lines the formula for sum of 3 cubes is as given in the answer earlier.
HTH



Director
Joined: 03 Jul 2003
Posts: 652

My Ans is E:
From 2: It can get many solutions. USELESS.
From (1) & (2) togather, we get two sets of numbers.
Both sets give different answers.
Thus, answer is E



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The correct answer is B.
(1) can be shown to be insufficient with a quick example as most of you have shown.
Many of you also said the (2) does not tell you anything. Did you even try any numbers? The answer will always be the same. Although that does not PROVE it, it would certainly give you a clue that there is a way to simplify the sum of cubes. (Frankly, on the real test, if I tried 4 different sets of simply numbers and they all worked, I would assume it is true). You can prove it as follows:
In (2), we are given a + b + c = 0. This means c = (a + b). Make this substitution in the sum of cubes, expand what used to be the c^3 term, then simplify. You will get (a+b)*3*a*b. Now substitute c for the (a+b) term and you will get 3*a*b*c.
If a + b + c = 0, then (a^3 + b^3 + c^3)/(abc) = 3abc/abc = 3 for ANY a, b, or c not equal to 0, hence B is the correct answer.
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AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993



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Re: If abc is not equal to 0, what is the value of (a^3 + b^3 + [#permalink]
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Re: If abc is not equal to 0, what is the value of (a^3 + b^3 +
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