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OG13 DS-Q15: What is cube root of W?

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OG13 DS-Q15: What is cube root of W?

by gmatstud » Sun Jun 24, 2012 2:51 am
Needed clarification on Q15 of OG13 Data Sufficiency section:

15. What is cube root of w
(1) The 5th root of w is 64
(2) The 15th root of w is 4

Here, when I look at explanation in OG, they have used exponent arithmetics to find the exact value of cube root.

What I wanted to know is that do we really need to see if we are getting an integer cube root ? Here it has not been mentioned whether w or cube root of w should be integer. It can be real number as well. For e.g. square root of 2 is 1.4xx . So the way I approached is that as we know 5th root of w, we should be able to find value of w (can be integer/real) and then from there cube root of w(again integer/real). Am I missing something here?
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by sandeep_thaparianz » Sun Jun 24, 2012 4:06 am
A) w^(1/5) =64
Which means w^(1/5) = 2^(6)
W= 2^(30)
Hence W^(1/3)=2^(10)

Sufficient

B) w^(1/15)=4=2^(2)
W=2^(30)
Hence W^(1/3)=2^(10)

Sufficient

Hence answer should be D? Hope it helps.
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by Anurag@Gurome » Sun Jun 24, 2012 4:24 am
gmatstud wrote:What I wanted to know is that do we really need to see if we are getting an integer cube root ? Here it has not been mentioned whether w or cube root of w should be integer. It can be real number as well. For e.g. square root of 2 is 1.4xx . So the way I approached is that as we know 5th root of w, we should be able to find value of w (can be integer/real) and then from there cube root of w(again integer/real). Am I missing something here?
Your approach is the ideal approach to tackle DS problems.

There is no need to find out the roots.
From both statements we can find a definite value for w and hence we can find the cube root of w. DS questions are all about identifying the sufficiency of the statements. No need to calculate everything blindly.
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by gmatstud » Tue Jun 26, 2012 2:52 am
Anurag@Gurome wrote:
gmatstud wrote:What I wanted to know is that do we really need to see if we are getting an integer cube root ? Here it has not been mentioned whether w or cube root of w should be integer. It can be real number as well. For e.g. square root of 2 is 1.4xx . So the way I approached is that as we know 5th root of w, we should be able to find value of w (can be integer/real) and then from there cube root of w(again integer/real). Am I missing something here?
Your approach is the ideal approach to tackle DS problems.

There is no need to find out the roots.
From both statements we can find a definite value for w and hence we can find the cube root of w. DS questions are all about identifying the sufficiency of the statements. No need to calculate everything blindly.
One clarification needed here:
- does it matter if w is integer or real number (decimals). For eg. square root of 2 is 1.4xxxx so do we even have to go that step of doing the calculations mentioned by sandeep_thaparianz

I mean even if (1) would have been that 5th root of w is 65, w can come out to a real number (decimal)
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by tutorphd » Tue Jun 26, 2012 3:33 am
The point in this problem is not about integer results but about reversibility of roots.

If you have any root of w, you can get what w is (integer or not integer, doesn't matter) by raising the root to the necessary power. This is possible because that is how any root (quadratic, cubic etc.) is defined: raised to the necessary power, it returns the original number under the root.

Once you have w, you can calculate any other root of it, as long as its allowed(quadratic root is not defined on negative numbers etc). If the root is allowed, it returns a single value, even the quadratic root: root(4) = + 2 only (not -2).
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by GMATGuruNY » Tue Jun 26, 2012 6:01 am
gmatstud wrote:Needed clarification on Q15 of OG13 Data Sufficiency section:

15. What is cube root of w
(1) The 5th root of w is 64
(2) The 15th root of w is 4

Here, when I look at explanation in OG, they have used exponent arithmetics to find the exact value of cube root.

What I wanted to know is that do we really need to see if we are getting an integer cube root ? Here it has not been mentioned whether w or cube root of w should be integer. It can be real number as well. For e.g. square root of 2 is 1.4xx . So the way I approached is that as we know 5th root of w, we should be able to find value of w (can be integer/real) and then from there cube root of w(again integer/real). Am I missing something here?
The math explanations in the OG do not always offer the best or most efficient approach -- especially for DS problems.
The explanations for DS problems typically will show all of the work required to answer the question.
But we should NOT be doing all of this work: as soon as we can see whether a statement is sufficient, we should move onto the next task at hand.
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by Anurag@Gurome » Tue Jun 26, 2012 6:20 am
gmatstud wrote:- does it matter if w is integer or real number (decimals).
No. It doesn't.
If we know that n-th root of w, we can always determine w for any w as long as we know the value of n.
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