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If a is not equal to b and a^3=b^2, what is the value of b^4 ?

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Kaushik786
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If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   Updated on: 08 Mar 2021, 05:07
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If a is not equal to b and a^3=b^2, what is the value of b^4 ?

1. a^(1/2) =4

2. 3b^2 - 2a^2 =160
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D

Originally posted by Kaushik786 on 07 Mar 2021, 11:31.
Last edited by Kaushik786 on 08 Mar 2021, 05:07, edited 2 times in total.
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AnirudhaS
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   07 Mar 2021, 14:34
\(a\neq{b}\) and \(a^3=b^3\)
how is that possible?
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Kaushik786
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   08 Mar 2021, 05:11
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Statement 1: Suff
a^1/2 = 4
a=16
b^2=a^3
b^2=16^3
b^4=16^6
Statement 2: Suff
3b^2-2a^2=160
b^2=a^3
3a^3-2a^2=160
a=4 satisfies the above equation
Therefore, a^3=b^2
b^4=a^6=4^6

Hence choice D.
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PujaBhattacharya
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   19 Jun 2021, 09:05
Kaushik786 wrote:
Statement 1: Suff
a^1/2 = 4
a=16
b^2=a^3
b^2=16^3
b^4=16^6
Statement 2: Suff
3b^2-2a^2=160
b^2=a^3
3a^3-2a^2=160
a=4 satisfies the above equation
Therefore, a^3=b^2
b^4=a^6=4^6

Hence choice D.


a=2 also satisfies the statement 2, so there are 2 possibilities. please clarify
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gmatgurulondon
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   01 Jul 2021, 05:24
Analyzing statement 2 is not helpful for the GMAT. A third-degree polynomial could potentially have multiple roots, and it's not easy to discount that possibility without a calculator. We just won't see a problem like this come up on the GMAT.
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SantoshN
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink] New post   01 Jul 2021, 07:21
Kaushik786 wrote:
Statement 1: Suff
a^1/2 = 4
a=16
b^2=a^3
b^2=16^3
b^4=16^6
Statement 2: Suff
3b^2-2a^2=160
b^2=a^3
3a^3-2a^2=160
a=4 satisfies the above equation
Therefore, a^3=b^2
b^4=a^6=4^6

Hence choice D.


Hai, Could you please explain how did you solve 3a^3-2a^2 =160 please .
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Re: If a is not equal to b and a^3=b^2, what is the value of b^4 ? [#permalink]
01 Jul 2021, 07:21
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