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# What is the cube root of w?

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Math Expert
Joined: 02 Sep 2009
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What is the cube root of w? [#permalink]

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06 Aug 2012, 03:15
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88% (00:41) correct 12% (00:56) wrong based on 1601 sessions

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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

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Re: What is the cube root of w? [#permalink]

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06 Aug 2012, 03:15
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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]

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06 Aug 2012, 03:31
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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]

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06 Aug 2012, 07:52
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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.
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Re: What is the cube root of w? [#permalink]

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05 Jun 2013, 03:56
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]

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30 May 2014, 01:55
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?
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Re: What is the cube root of w? [#permalink]

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30 Jul 2016, 08:36
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Bunuel wrote:
What is the cube root of w?

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

We need to determine the cube root of w. Thus, if we have a value for w, we can determine the value of the cube root of w.

Statement One Alone:

The 5th root of w is 64.

Recall that the nth root of a number is the number raised to the 1/n power; we can set up an equation with the information from statement one.

w^(1/5) = 64

Now raise both sides of the equation to the 5th power.

w = 64^5

Since we know that we have a unique value for w, we can stop here. This is enough information to enable us to determine the value of the cube root of w. Statement one provides enough information to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The 15th root of w is 4.

We can set up an equation with the information from statement two.

w^(1/15) = 4

w = 4^15

Since we know that we have a unique value for w, we can stop here. This is enough information to enable us to determine the value of the cube root of w. Statement two is also sufficient.

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Re: What is the cube root of w? [#permalink]

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25 Sep 2017, 17:32
b2bt wrote:
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?

Can anyone answer this? I have the same question.
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Re: What is the cube root of w? [#permalink]

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09 Feb 2018, 17:13
Hi guys

what if we are given that 6th root of W is 64. In that case can we say w= 64^(6)? or will we say that modulus W = 64^(6). The clarification is more towards what if we are given even number instead of an odd number than can we concretely find the value of w by multiplying with an exponential power on both sides.
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Re: What is the cube root of w? [#permalink]

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09 Feb 2018, 22:32
Rocket7 wrote:
Hi guys

what if we are given that 6th root of W is 64. In that case can we say w= 64^(6)? or will we say that modulus W = 64^(6). The clarification is more towards what if we are given even number instead of an odd number than can we concretely find the value of w by multiplying with an exponential power on both sides.

If $$\sqrt[6]{w}=64$$, then $$w = 64^6$$ only. w cannot be negative (w cannot be -64^6) because even roots from negative numbers are not defined for the GMAT.
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Re: What is the cube root of w? [#permalink]

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09 Feb 2018, 22:34
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Rocket7 wrote:
Hi guys

what if we are given that 6th root of W is 64. In that case can we say w= 64^(6)? or will we say that modulus W = 64^(6). The clarification is more towards what if we are given even number instead of an odd number than can we concretely find the value of w by multiplying with an exponential power on both sides.

Hi

If the question talks about roots (not powers) then the answer will be only one. So if it says:
6th root of W = 64, then W = 64^6

We cannot say |W| = 64^6, because then we have to take a case where W = - 64^6, but then 6th root (or any even root) of a negative number is not defined.

If instead the question says: 6th power of W is 64, here we are given W^6 = 64 or W^6 = 2^6
Here definitely there will be two cases: W can be = 2 or W can be = -2; because both 2^6 and (-2)^6 give the same result, 64.
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Re: What is the cube root of w? [#permalink]

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21 Apr 2018, 07:19
mandyrhtdm wrote:
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.

pushpitkc how do we call this process mathematically w = 64^3 = 4^15 = 2^30 exponential expansion or

And how from this 64^3 we get this 4^15 ?

many many thanks
Math Expert
Joined: 02 Sep 2009
Posts: 44639
Re: What is the cube root of w? [#permalink]

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21 Apr 2018, 07:25
dave13 wrote:
mandyrhtdm wrote:
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.

pushpitkc how do we call this process mathematically w = 64^3 = 4^15 = 2^30 exponential expansion or

And how from this 64^3 we get this 4^15 ?

many many thanks

$$64^3 = (2^6)^3 = 2^{6*3} = 2^{18}$$
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Re: What is the cube root of w?   [#permalink] 21 Apr 2018, 07:25
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