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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a and b are positive integers, then what is the value of a^b ?

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Math Expert V
Joined: 02 Sep 2009
Posts: 60727
If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 42% (01:38) correct 58% (01:38) wrong based on 50 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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Math Expert V
Joined: 02 Aug 2009
Posts: 8327
Re: If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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1
If a and b are positive integers, then what is the value of $$a^b$$?

(1) $$b^a = 27$$
27=27^1....a^b=1^27=1
27=3^3......a^b=3^3=27
Insufficient

(2) $$a^{2b} = 729$$
729=3^6=3^{2*3}....a^b=3^3=27
729=27^2=27^{2*1}.....a^b=27^1=27
No other way that power is EVEN
Sufficient

B
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Manager  S
Joined: 06 May 2019
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Location: India
Schools: LBS '22
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If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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

(1) b2a=27

: b = 3 or 27, a = 3 or 1 ....so a^b is coming 27 or 1 --- NS

(2) a2b=729

: a = 3 or 27 , b = 3 or 1 ...so a^b is coming 27 only .. Sufficient

Senior Manager  P
Joined: 25 Jul 2018
Posts: 491
Re: If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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Statement1: Clearly insufficient

(Statement2):$$(a^{b}—27)(a^{b}+27)=0$$

—>$$a^{b} = 27$$

Sufficient

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Intern  B
Joined: 13 Nov 2018
Posts: 5
Re: If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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In statement 1, $$b^a$$ = 27 means b = 3 and a= 3 OR b = 27 and a = 1.
So, $$a^b$$ can be either 27 or 1.

Statement 1 is insufficient, so B or C or E.

In statement 2, $$a^{2b}$$ = 729. This can be rewritten as $$(a^b)^2$$ = 729. This is only possible when $$a^b$$ = 27 (considering that a and b are positive integers and hence -27 can safely be ignored)
Statement 2 is sufficient. So, B is the correct answer.

Cheers! Re: If a and b are positive integers, then what is the value of a^b ?   [#permalink] 15 Nov 2019, 11:34
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