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cube root

by ska7945 » Sun Aug 17, 2008 3:52 pm
What is the cube root of w ?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.



ans D
how would you solve for B?
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by Suyog » Sun Aug 17, 2008 4:13 pm
I dont think so u've to slove it.
By just looking at (I) & (II), one can determine that they both alone are sufficient.
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by pranavc » Sun Aug 17, 2008 4:32 pm
For B, equate 4^15 = w

This is the same as 2^30 = w
=> (2^10)^3 = w

Hence, the cube root of w is 2^10. Hope this helps.
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pranavc

by ska7945 » Sun Aug 17, 2008 6:51 pm
i think you misunderstood the Qs.
i asked how you solve x^15=4
just like A, 2^5=64
so anybody?
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Re: pranavc

by Ian Stewart » Sun Aug 17, 2008 7:40 pm
ska7945 wrote:i think you misunderstood the Qs.
i asked how you solve x^15=4
just like A, 2^5=64
so anybody?
The question is not asking you to solve x^15 = 4. It says that the 15th root of x (well, it says w, but I'll use x) is 4, so you would be solving:

x^(1/15) = 4

which is what pranavc has already done. In more detail- raise both sides to the power 15, and you have

x = 4^(15) = (2^2)^(15) = 2^(30)

The cube root of x is equal to x^(1/3). Since x = 2^(30),

x^(1/3) = (2^(30))^(1/3) = 2^(10) = 1028

Of course, as Suyog pointed out, it's a Data Sufficiency question, so there's no advantage to actually solving the question. As soon as you see you'll get a single numerical answer for x, you can stop working.

Incidentally, if the question did ask you to solve

x^15=4

then x would be equal to 4^(1/15). You can't write that any more simply.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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