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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.

Post your Blog on GMATClub We would like to invite all applicants who are applying to BSchools this year and are documenting their application experiences on their blogs to...

HBS alum talks about effective altruism and founding and ultimately closing MBAs Across America at TED: Casey Gerald speaks at TED2016 – Dream, February 15-19, 2016, Vancouver Convention Center...