What is the cube root of w ? : GMAT Data Sufficiency (DS)
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# What is the cube root of w ?

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Joined: 31 Dec 1969
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What is the cube root of w ? [#permalink]

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25 Oct 2004, 20:14
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83% (01:26) correct 17% (00:38) wrong based on 162 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: what-is-the-cube-root-of-w-136884.html
[Reveal] Spoiler: OA
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
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25 Oct 2004, 20:32
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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?!
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25 Oct 2004, 20:34
Oh I forgot to log in the second guest was moi! Whoops!
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26 Oct 2004, 14:56

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: Technology, Entrepreneurship
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
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Kudos [?]: 199 [0], given: 102197

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26 Oct 2004, 15:36
doggita wrote:

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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26 Oct 2004, 18:25
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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
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DS: cube root of w [#permalink]

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30 Apr 2006, 07:09
What is the cube root of w?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.
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30 Apr 2006, 08:42
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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30 Apr 2006, 12:35
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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...!
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30 Apr 2006, 17:35
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!
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30 Apr 2006, 18:28
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'.
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30 Apr 2006, 18:42
Yes this is a definite D
can be solved from both (1) and (2)
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01 May 2006, 00:52
Does anybody have more clear explanation please?
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01 May 2006, 00:58
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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!
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08 May 2006, 05:56
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.
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08 May 2006, 07:34
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
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08 May 2006, 18:08
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
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08 May 2006, 18:58
St1:

w^1/5 = 64 --> can find w and therefore w^1/3

St2:
Same as above.

Ans D
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09 May 2006, 08:05
Both statements are sufficient, since we can find the value of w from both of them
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Re: DS: cube root of w [#permalink]

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09 May 2006, 19:39
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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, 19:39

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