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Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

What is the cube root of w ? [#permalink]
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25 Oct 2004, 21:14
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84% (01:25) correct
16% (00:38) wrong based on 176 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. OPEN DISCUSSION OF THIS QUESTION IS HERE: whatisthecuberootofw136884.html
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Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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I think the answer is D as both statements give the same answer.
64 raised to the power 5 is the same as 4 raised to the power 15 i.e 64^5 is the same as (4^3)^5 = 4^15 same as statement 2.
For the working: Now the cube root of 4^15 will be (4^15)^1/3 i.e. 15 times 1/3=5 (just for kicks is 1024) Hope this helps! If I am wrong pls can someone correct me?!



Manager
Joined: 09 Sep 2004
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Oh I forgot to log in the second guest was moi! Whoops!



Manager
Joined: 21 Jul 2004
Posts: 120

agree w/ the answer, D.
one thing we need to be more careful is that if the given is "even" root... w could be negative...



Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

doggita wrote:
agree w/ the answer, D.
one thing we need to be more careful is that if the given is "even" root... w could be negative...
thanks doggita for the reminder!



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Joined: 16 Oct 2003
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D.
I.
w^1/5 = 64
w = 64^5
w^1/3=64^5/3 = 4^5
II.
w^1/15 = 4
w = 4^15
w^1/3 = 4^15/3 = 4^5



Senior Manager
Joined: 08 Jun 2004
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Location: Europe

DS: cube root of w [#permalink]
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30 Apr 2006, 08:09
What is the cube root of w?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.



VP
Joined: 28 Mar 2006
Posts: 1369

D...
w^1/5 = 2^6 from A
w^1/15 = 2^2 from B
We can get cube root from either of them



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Joined: 05 Jan 2006
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fifth root and fifteenth root both will give us definateve answer so cube root can be found from both!
so D...
if it's 4 or 14th root than we may have + two posibility...!



VP
Joined: 29 Apr 2003
Posts: 1403

Agreed its D! Is the root is of an odd number, then the sign is restored. Since both 5 and 15 are off, we can compute w and hence calculate the 3rd root!



Manager
Joined: 14 Mar 2006
Posts: 208

sm176811 wrote: Agreed its D! Is the root is of an odd number, then the sign is restored. Since both 5 and 15 are off, we can compute w and hence calculate the 3rd root!
agree with D. almost forgot about the 'evil evens'.



Manager
Joined: 17 Jan 2006
Posts: 92

Yes this is a definite D
can be solved from both (1) and (2)



Senior Manager
Joined: 08 Jun 2004
Posts: 495
Location: Europe

Does anybody have more clear explanation please?



VP
Joined: 29 Apr 2003
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x^n (where n is even) looses its sign ie 2^2 and 2^2 is the same.
So u cannot find the square root and get the exact value of the original number...
But when n is odd u CAN!
So in the given options, both the roots are odd! Hence u can get the value of w from both!
Hence u can calculate the cube of w from both!



Intern
Joined: 03 May 2006
Posts: 27

Surely its D. From statement 1, taking each side to the power of (5/3), we get the cube root as 1024. Again from statement 2, taking each side to the power of 5, we get the same answer. Hence the result follows.



Director
Joined: 10 Oct 2005
Posts: 718
Location: Madrid

1st The 5th root of w is 64. hence w=64^5
cube root of 64^5 suff
2 st w=4^15 from here we can figure out cube root of w hence suff
D it is
_________________
IE IMBA 2010



Manager
Joined: 11 Oct 2005
Posts: 94

Either works the answer is D
5 rt(w) = 64
so removing the cube rt from the left means raising 64^5 which gives 1073741824
From 2
15 rt(w) = 4
Same method here raise both sides to 15 to find out what w is
Ans is the same 1073741824
so D



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

St1:
w^1/5 = 64 > can find w and therefore w^1/3
St2:
Same as above.
Ans D



Senior Manager
Joined: 29 Jun 2005
Posts: 403

The answer should be D
Both statements are sufficient, since we can find the value of w from both of them



VP
Joined: 29 Dec 2005
Posts: 1341

Re: DS: cube root of w [#permalink]
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09 May 2006, 20:39
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M8 wrote: What is the cube root of w? (1) The 5th root of w is 64. (2) The 15th root of w is 4.
(1) w^1/5 = 64
w^(1/5)(5) = 64^5
w = 64^5
w = (4^15)
w^1/3 = 4^(1/3)(15)
w^1/3 = 4^5
(2) w^1/15 = 4
w = 4^15
w^1/3 = 4^(1/3)(15)
w^1/3 = 4^5
so D...




Re: DS: cube root of w
[#permalink]
09 May 2006, 20:39



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