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

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Posts: 60727
If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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New post 15 Nov 2019, 02:05
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

42% (01:38) correct 58% (01:38) wrong based on 50 sessions

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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 15 Nov 2019, 07:29
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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If a and b are positive integers, then what is the value of a^b ?  [#permalink]

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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]

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New post 15 Nov 2019, 09:00
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]

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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.

Cheers!
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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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