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Both a and b are positive; what is the value of a?

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Source: — Data Sufficiency |
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by gmatmachoman » Tue Jul 13, 2010 10:01 am
deepak_free wrote:Both a and b are positive; what is the value of a?

(1) 150 percent of a equals 450 percent of b.

(2) ab is the cube of a positive integer.

st 1: Insufficient

a= 3b

st 2:

ab = X^3

Insufficient

Combining st 1 & st 2;
we have 3b^2 = X^3

solving for X = 3
we get b =3,a=9
Pick C
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by deepak_free » Tue Jul 13, 2010 10:09 am
Do you really think

3b^2=X^3

will result only in 3 even if it is not provided that x is an integer
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by barcebal » Tue Jul 13, 2010 10:13 am
Just because, when combining statements 1 and 2, the cube root of 3b^2 equals an integer doesn't mean that b has to be 3.

B could also be 81.

3(81^2)=27^3

Therefore both are insufficient.

Hope that helps.
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by gmatmachoman » Tue Jul 13, 2010 10:14 am
deepak_free wrote:Do you really think

3b^2=X^3

will result only in 3 even if it is not provided that x is an integer
The st 2 says that X is a positive integer..is n't it???
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by outreach » Tue Jul 13, 2010 11:29 am
if b=81 then a=27
now 2781 is not a cube root of any number
so it will be incorrect..
any opinion on the same??

barcebal wrote:Just because, when combining statements 1 and 2, the cube root of 3b^2 equals an integer doesn't mean that b has to be 3.

B could also be 81.

3(81^2)=27^3

Therefore both are insufficient.

Hope that helps.
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by barcebal » Tue Jul 13, 2010 11:42 am
outreach wrote:if b=81 then a=27
now 2781 is not a cube root of any number
so it will be incorrect..
any opinion on the same??

barcebal wrote:Just because, when combining statements 1 and 2, the cube root of 3b^2 equals an integer doesn't mean that b has to be 3.

B could also be 81.

3(81^2)=27^3

Therefore both are insufficient.

Hope that helps.
A is 3 times b, not the other way around.

So if B is 81, then a is actually 243 and AB=19683, and the cube root of that is 27.
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