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If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) [#permalink]
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22 Mar 2011, 11:05
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If abc ≠ 0, what is the value of \(\frac{a^3 + b^3 + c^3}{abc}\) ? (1) \(a=1, b=2, c=3\) (2) \(a + b + c = 0\)
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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 11:28
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Statement 1: a=1, b=2, c=3 So a, b, c can be positive or negative. Thus, the value of the expression cannot be uniquely determined. NS Statement 2: a + b + c = 0 (a + b + c)^3 = a^3 + b^3 + c^3 + (3ab + 3bc + 3ca) (a + b + c) – 3abc Substitute for a + b + c = 0 in the above equation: 0 = a^3 + b^3 + c^3  3abc => 3abc = a^3 + b^3 + c^3 => (a^3 + b^3 + c^3)/abc = 3 Sufficient
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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 11:29
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since abc ≠ 0 , we know that either all numbers can be +ve or any two can be ve
Option A does not help to solve the problem since we can not make out that which numbers can be ve and value changes with every trial and error method. Therefore, A can not be the answer.
Option B tells us that A+B+C=0, therefore we can use the formula that
\(a^3 + b^3 + C^3  3abc = (a+b+c) (a^2 + b^2 + c^2  ab  bc  ac)\)
and since we know that a+b+c = 0 then \(a^3 + b^3 + c^3 = 3abc\)
And thus putting "3abc" at the place of \(a^3 + b^3 + c^3\), will give us the answer. Therefore answer is "B"
Only thing that since I know the formula thats why I could solve this problem within seconds ..... how to solve if we do not know the formula .... please someone explain.



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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 11:30



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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 11:31
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gmatpapa wrote: If abc ≠ 0, what is the value of \(\frac{a^3 + b^3 + c^3}{abc}\) ?
(1) \(a=1, b=2, c=3\) (2) \(a + b + c = 0\) \(a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2abbcac)+3abc\) Using statement 2 & the above formula: \(\frac{a^3 + b^3 + c^3}{abc} = \frac{(a+b+c)(a^2+b^2+c^2abbcac)}{abc}+\frac{3abc}{abc} = 0+3=3\) Sufficient. Ans: "B"
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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 11:32
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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 18:57
1. Not sufficient as there more than one possible combination for a, b and c that satisfies the given equation.
2. Sufficient by solving the given equation we can see that (a+b+c)^3 = a3+b3+c33abc
=> a3+b3+c3 = 3abc , enough to answer the question.
Answer is B.



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Re: Inequalities and modules DS [#permalink]
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22 Mar 2011, 19:31
To add some more, this has been posted earlier, please take a look at the solution step suggesting c = (a+b). ds1543.html
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Re: Inequalities and modules DS [#permalink]
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23 Mar 2011, 07:23
I seriously don't know how to use this in real life. I am not good in algebra. Not my style



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Re: If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) [#permalink]
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27 Jun 2016, 21:50
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gmatpapa wrote: If abc ≠ 0, what is the value of \(\frac{a^3 + b^3 + c^3}{abc}\) ?
(1) \(a=1, b=2, c=3\) (2) \(a + b + c = 0\) Alternative approach statement 1: Clearly there are many different values that will lead to various results . Insuff statement 2: we plug numbers that stefiey the fact a+b+c=0 a=1, b= 1, c=2........apply in question stem (1+18)/2= 6/2=3 a=1, b=2, c=3.........apply in question stem (1+827)/6=18/6=3 a=1, b=3, c=4.........apply in question stem (1+2764)/12= 36/12=3 clearly the answer is B



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Re: If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) [#permalink]
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19 Oct 2017, 06:33
AmrithS wrote: By the way, are we expected to know these equations for GMAT? I'm bumping this question. This would be difficult to complete in a timed environment. Experts, is this a realistic problem on the gmat? Posted from my mobile device




Re: If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1)
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19 Oct 2017, 06:33






