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# What is the cube root of w?

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Math Expert
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What is the cube root of w? [#permalink]  06 Aug 2012, 02:15
Expert's post
3
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BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:43) correct 15% (00:59) wrong based on 586 sessions
What is the cube root of w?

(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

Practice Questions
Question: 15
Page: 276
Difficulty: 600
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47483 [3] , given: 7123

Re: What is the cube root of w? [#permalink]  06 Aug 2012, 02:15
3
KUDOS
Expert's post
SOLUTION

What is the cube root of w?

(1) The 5th root of w is 64 --> $$\sqrt[5]{w}=64$$ --> we can find $$w$$, hence we can find $$\sqrt[3]{w}$$: $$w=64^5$$ --> $$\sqrt[3]{w}=\sqrt[3]{64^5}$$. Sufficient.

(2) The 15th root of w is 4 --> $$\sqrt[15]{w}=4$$. The same here. Sufficient.

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Re: What is the cube root of w? [#permalink]  06 Aug 2012, 02:31
4
KUDOS
1
This post was
BOOKMARKED
1. If the nth root is asked for a number X:
If n is odd - It has a unique solution that satisfies.
On the other hand, if n is even - then both (y)^n and (-y)^n satisfies the solution.
Now to the problem:
A - sufficient. 5th root - 5 odd.
B - sufficient. - 15 -odd.

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Re: What is the cube root of w? [#permalink]  06 Aug 2012, 06:52
1
KUDOS
This is a simple Surd problem i will rate its difficulty at 500 or below.
as the first step break all numbers down to their basic form 64 = 4^3 = 2^6 ( we will find later that the second part is not necessary in this question, but in some other question we might need to break down further)
Lets take statement 1 : (w)^1/3 = 64 this means w = 64^3 = 4^15 = 2^30 ( stop ! much before this coz you knwo you can find it )
Second statement (w)^1/15 = 4 This means w = 4^15 = 2^30 ( Stop as soon as you know it is solvable)
So choice D is the nswer.
Math Expert
Joined: 02 Sep 2009
Posts: 28781
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Kudos [?]: 47483 [0], given: 7123

Re: What is the cube root of w? [#permalink]  10 Aug 2012, 04:10
Expert's post
SOLUTION

What is the cube root of w?

(1) The 5th root of w is 64 --> $$\sqrt[5]{w}=64$$ --> we can find $$w$$, hence we can find $$\sqrt[3]{w}$$: $$w=64^5$$ --> $$\sqrt[3]{w}=\sqrt[3]{64^5}$$. Sufficient.

(2) The 15th root of w is 4 --> $$\sqrt[15]{w}=4$$. The same here. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 28781
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Kudos [?]: 47483 [0], given: 7123

Re: What is the cube root of w? [#permalink]  05 Jun 2013, 02:56
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on roots problems: math-number-theory-88376.html

All DS roots problems to practice: search.php?search_id=tag&tag_id=49
All PS roots problems to practice: search.php?search_id=tag&tag_id=113

Tough and tricky exponents and roots questions (DS): tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky exponents and roots questions (PS): new-tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: What is the cube root of w? [#permalink]  30 May 2014, 00:55
The answer would still be D if
1. square root of w was asked with same statements
2. cube root of w and (1) and (2) had even roots.

But answer would be E if
All the roots in question were even

Am I correct?
Re: What is the cube root of w?   [#permalink] 30 May 2014, 00:55
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