Algebra - a question from prep swift under the topic Equivalent Equation

GRE Quant Problem Solving
1

I couldn’t figured out why the answer is C instead of D

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For this type of question where there’s no fixed parameter or given, I like to plonk in a number to prevent myself from getting caught off guard

If X = -3, A = undefined and B = -3
If X = 0, A = B = 0
If X = 3, A = B = 3

Since ETS doesn’t recognise a negative term within a radical and X^3 = -3 x -3 x -3 = -27, wouldn’t the answer is we can’t determine the relationship?

Thank you in advance.

2

Quantity A can be simplified as:

\sqrt[3]{x^3} = (x^3)^{\frac{1}{3}} = x^{(3 \times \frac{1}{3})} = x^1=x
3

That’s your mistake.

4

Haha I missed the obvious and cracked my head for nothing. Thanks for the light (as well as your replies in other threads which I will get to it - thank you for taking time).

Just a quick question - seems like for questions with open parameter, I should just reduce or simplify a given term as much as I could before I plonk in numbers to test its range of possible values. Would you agree?

5

:laughing:

Similar to my reply to HoldMyBeer (what a name!), do you think for questions with an open parameter, I should just reduce or simplify a given term as much as I could before I plonk in numbers to test its range of possible values. What do you think?

6

It isn’t necessary, but can usually help, as long as the steps you take in simplifying are themselves legal.