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

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Bunuel
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If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  15 Nov 2019, 02:05
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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] New post  15 Nov 2019, 07:29
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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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If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  15 Nov 2019, 08:45
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


Answer is B
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Re: If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  15 Nov 2019, 09:00
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Statement1: Clearly insufficient

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

—>\( a^{b} = 27\)

Sufficient

The answer is B

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

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Re: If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  23 Jun 2020, 19:01
Bunuel wrote:
If a and b are positive integers, then what is the value of \(a^b\)?


(1) \(b^a = 27\)

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


S1: a=1, b=27 and a=3, b=3 both work. NOT SUFFICIENT.

S2: Since we're limited to integers, a=27, b=1 is the only possible solution. SUFFICIENT.

ANSWER: B
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Re: If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  27 Jul 2020, 07:34
Papist wrote:
Bunuel wrote:
If a and b are positive integers, then what is the value of \(a^b\)?


(1) \(b^a = 27\)

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


S1: a=1, b=27 and a=3, b=3 both work. NOT SUFFICIENT.

S2: Since we're limited to integers, a=27, b=1 is the only possible solution. SUFFICIENT.

ANSWER: B

Actually, for statement 2, a=3 & b=3 is also a possible solution. Coincidentally, both pairs of solutions lead to the final answer being 27.
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Re: If a and b are positive integers, then what is the value of a^b ? [#permalink] New post  29 Nov 2022, 00:56
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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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