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If a and b are positive integers, then what is the value of a^b?

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If a and b are positive integers, then what is the value of a^b?  [#permalink]

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New post 05 Oct 2016, 00:26
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If a and b are positive integers, then what is the value of \(a^b\)?

(1) \(b^a = 27\)
(2) \(a^{2b} = 729\)

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Re: If a and b are positive integers, then what is the value of a^b?  [#permalink]

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New post 05 Oct 2016, 01:29
idontknowwhy94 wrote:
If a and b are positive integers, then what is the value of \(a^b\)?

1. \(b^a = 27\)
2. \(a^{2b} = 729\)



According to Statement 1
b^a=27 this can be satisfied with a=3 b=3 and a=1 and b=27
Hence a^b will have 2 different values of 27 and 1 Not sufficient

According to statement 2
a^(2b)=729 this can be written as 27^(2b)= 27^2 so in this case a=27 b=1
a^(2b)= 3^6 in this case a=3 b=3
These are the only 2 possible positive integer values as a and b are positive integers
either way you get a^b=27 Hence sufficient
Answer B
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Re: If a and b are positive integers, then what is the value of a^b?  [#permalink]

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New post 26 Sep 2017, 12:10
idontknowwhy94 wrote:
If a and b are positive integers, then what is the value of \(a^b\)?

(1) \(b^a = 27\)
(2) \(a^{2b} = 729\)


Statement 1: two variable one equation, hence multiple solutions are possible for e.g \(a=1\), \(b=27\) or \(a=3\), \(b=3\). Hence Insufficient

Statement 2: \(a^{2b}=729\), or \((a^b)^2=729\). take square root of both sides

\(a^b=27\). Sufficient

Option B
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Re: If a and b are positive integers, then what is the value of a^b? &nbs [#permalink] 26 Sep 2017, 12:10
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