Last visit was: 03 Aug 2024, 05:51 It is currently 03 Aug 2024, 05:51
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# What is the cube root of w?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646239 [42]
Given Kudos: 86843
Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646239 [12]
Given Kudos: 86843
Intern
Joined: 14 Dec 2010
Posts: 3
Own Kudos [?]: 11 [11]
Given Kudos: 0
General Discussion
Manager
Joined: 05 Jul 2012
Posts: 53
Own Kudos [?]: 150 [2]
Given Kudos: 8
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE:Engineering (Energy and Utilities)
Re: What is the cube root of w? [#permalink]
2
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.
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6656 [10]
Given Kudos: 1646
Re: What is the cube root of w? [#permalink]
8
Kudos
2
Bookmarks
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.

Manager
Joined: 24 Sep 2011
Posts: 82
Own Kudos [?]: 87 [0]
Given Kudos: 47
Re: What is the cube root of w? [#permalink]
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.
Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646239 [0]
Given Kudos: 86843
Re: What is the cube root of w? [#permalink]
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.
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2557 [1]
Given Kudos: 459
Location: India
Re: What is the cube root of w? [#permalink]
1
Bookmarks
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.
VP
Joined: 09 Mar 2016
Posts: 1142
Own Kudos [?]: 1030 [0]
Given Kudos: 3851
Re: What is the cube root of w? [#permalink]
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: 94776
Own Kudos [?]: 646239 [1]
Given Kudos: 86843
Re: What is the cube root of w? [#permalink]
1
Kudos
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

$$64^3 = (2^6)^3 = 2^{6*3} = 2^{18}$$
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30924 [2]
Given Kudos: 799
Re: What is the cube root of w? [#permalink]
2
Bookmarks
Top Contributor
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.

Target question: What is the cube root of w?

Statement 1: The 5th root of w is 64.
ASIDE: If the square root of x = 7, then x = 7²
If the cube root of x = 10, then x = 10³
If the fourth root of x = 6, then x = 6⁴
etc

So, if the 5th root of w is 64, then w = 64⁵
Since we COULD determine the actual value of w, we COULD find the cube root of w
In other words, we have all of the information we need to answer the target question with certainty
Statement 1 is SUFFICIENT

Statement 2: The 15th root of w is 4
From this we can conclude that w = 4¹⁵
Since we COULD determine the actual value of w, we COULD find the cube root of w
In other words, we have all of the information we need to answer the target question with certainty
Statement 2 is SUFFICIENT

Cheers,
Brent
Non-Human User
Joined: 09 Sep 2013
Posts: 34222
Own Kudos [?]: 857 [0]
Given Kudos: 0
Re: What is the cube root of w? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: What is the cube root of w? [#permalink]
Moderator:
Math Expert
94776 posts