What is the cube root of w? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 06:42

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the cube root of w?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7090

Kudos [?]: 93316 [0], given: 10557

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

### Show Tags

06 Aug 2012, 02:15
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (01:42) correct 15% (00:59) wrong based on 1068 sessions

### HideShow timer Statistics

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: 36590
Followers: 7090

Kudos [?]: 93316 [3] , given: 10557

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

### Show Tags

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.

_________________
Intern
Joined: 14 Dec 2010
Posts: 3
Followers: 0

Kudos [?]: 6 [5] , given: 0

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

### Show Tags

06 Aug 2012, 02:31
5
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.

Manager
Joined: 05 Jul 2012
Posts: 81
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Followers: 4

Kudos [?]: 40 [1] , given: 8

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

### Show Tags

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: 36590
Followers: 7090

Kudos [?]: 93316 [0], given: 10557

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

### Show Tags

10 Aug 2012, 04:10
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: 36590
Followers: 7090

Kudos [?]: 93316 [0], given: 10557

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

### Show Tags

05 Jun 2013, 02:56
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

_________________
Current Student
Joined: 25 Sep 2012
Posts: 300
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Followers: 2

Kudos [?]: 133 [0], given: 242

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

### Show Tags

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?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13476
Followers: 576

Kudos [?]: 163 [0], given: 0

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

### Show Tags

05 Dec 2015, 19:12
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.
_________________
Senior Manager
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 464
Followers: 22

Kudos [?]: 193 [2] , given: 2

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

### Show Tags

30 Jul 2016, 07:36
2
KUDOS
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.

_________________

Jeffrey Miller
Jeffrey Miller

Re: What is the cube root of w?   [#permalink] 30 Jul 2016, 07:36
Similar topics Replies Last post
Similar
Topics:
2 Is the nth root of n greater than the cube root of 3? 4 04 Feb 2016, 17:18
9 What is the volume of a certain cube? 8 10 Dec 2013, 13:12
8 If x and y are positive integers, is the following cube root 5 09 Jun 2012, 06:22
What is the surface area of the cube ? 4 26 Jul 2011, 05:42
6 What is the volume of the cube above? 9 26 Oct 2010, 08:07
Display posts from previous: Sort by