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

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Manager
Joined: 03 Oct 2016
Posts: 83
Concentration: Technology, General Management
WE: Information Technology (Computer Software)
If a and b are positive integers, then what is the value of a^b?  [#permalink]

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05 Oct 2016, 00:26
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75% (hard)

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44% (01:16) correct 56% (01:12) wrong based on 75 sessions

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

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