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What is the value of a^3 + a^2b + ab^2 + b^3?

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by Max@Math Revolution » Thu Mar 12, 2020 12:08 am

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Answers

A

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E

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Difficulty—

[GMAT math practice question]

What is the value of a^3 + a^2b + ab^2 + b^3?

1) a + b = 2 \(\sqrt{2}\) , ab = 1
2) a = \(\sqrt{2}\) +1
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Source: — Data Sufficiency |
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Re: What is the value of a^3 + a^2b + ab^2 + b^3?

by Max@Math Revolution » Fri Mar 13, 2020 1:41 am
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We have
a^3 + a^2b + ab^2 + b^3
= a^3 + 3a^2b + 3ab^2 + b^3 - (2a^2b + 2ab^2)
= (a + b)^3 – (2a^2b + 2ab^2)
= (a + b)^3 – 2ab(a + b)

Then we have a^3 + a^2b + ab^2 + b^3 = (a+b)^3 – 2ab(a + b) = (2 \(\sqrt{2}\) )^3 – 2*1*( 2\(\sqrt{2}\)) = 16\(\sqrt{2}\) - 4\(\sqrt{2}\) = 12\(\sqrt{2}\) from condition 1).

Thus, condition 1) is sufficient. since condition 1) has 2 equations

Condition 2)
Since we don’t have any information about b, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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