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# What is the cube root of z? (1) The 5th root of z is 243. (2) The 25

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Re: What is the cube root of z? (1) The 5th root of z is 243. (2) The 25 [#permalink]
Bunuel wrote:
What is the cube root of z?

(1) The 5th root of z is 243.

(2) The 25th root of z is 3.

Similar question to practice: https://gmatclub.com/forum/what-is-the- ... 36884.html
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Re: What is the cube root of z? (1) The 5th root of z is 243. (2) The 25 [#permalink]
Bunuel wrote:
What is the cube root of z?

(1) The 5th root of z is 243.

(2) The 25th root of z is 3.

Official Explanation

The question asks us for the cube root of z, which is $$\sqrt[3]{z}$$ or $$z^{\frac{1}{3}}$$. Let's evaluate the data statements separately. Statement (1) tells us that $$z^{\frac{1}{5}}=243$$.

We can take both sides of the equation to the 5/3 power in order to try to massage this equation to give us what we are looking for:

$$(z^{\frac{1}{5}})^{\frac{5}{3}}=243^{\frac{5}{3}}$$

$$z^{\frac{1}{3}}=243^{\frac{5}{3}}$$

So, we've been given exactly what we are looking for: the value of $$z^{\frac{1}{3}}$$. It's equal to $$243^{\frac{5}{3}}$$. Therefore, Statement (1) is sufficient. Statement (2) is sufficient according to identical logic.

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Re: What is the cube root of z? (1) The 5th root of z is 243. (2) The 25 [#permalink]
Bunuel wrote:
What is the cube root of z?

(1) The 5th root of z is 243.

(2) The 25th root of z is 3.

Video Explanation

Re: What is the cube root of z? (1) The 5th root of z is 243. (2) The 25 [#permalink]
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