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What is the cube root of w?

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What is the cube root of w? [#permalink] New post 06 Aug 2012, 02:15
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3
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (01:43) correct 15% (00:59) wrong based on 586 sessions
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Re: What is the cube root of w? [#permalink] New post 06 Aug 2012, 02:15
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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.

Answer: D.
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Re: What is the cube root of w? [#permalink] New post 06 Aug 2012, 02:31
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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.

Answer D.
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Re: What is the cube root of w? [#permalink] New post 06 Aug 2012, 06:52
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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] New post 10 Aug 2012, 04:10
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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.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Expert Post
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Kudos [?]: 47483 [0], given: 7123

Re: What is the cube root of w? [#permalink] New post 05 Jun 2013, 02:56
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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

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: What is the cube root of w? [#permalink] New post 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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