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a^b=c If a, b and c are integers, what is the value of a?

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

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New post 07 Mar 2014, 00:33
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A
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E

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\(a^b=c\)

If a, b and c are integers, what is the value of a?

(1) c=1

(2) b≠0
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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New post 07 Mar 2014, 00:38
idinuv wrote:
\(a^b=c\)

If a, b and c are integers, what is the value of a?

(1) c=1

(2) b≠0


Even when we combine the statements we have \(a^b=1\), where b≠0, which is insufficient to get the value of a, for example: a=1, b=1 or a=-1. b=2.

Answer: E.
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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New post 07 Mar 2014, 00:55
idinuv wrote:
\(a^b=c\)

If a, b and c are integers, what is the value of a?

(1) c=1

(2) b≠0


Combining is insufficient:

a = 1, b = 1, c = 1
a = -1, b= 2, c = 1
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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New post 27 Jun 2017, 02:20
_shashank_shekhar_ wrote:
a^b=c

If a, b and c are integers, what is the value of a?

(1) c=1

(2) b≠0

Plz someone explain the solution.


Statement 1 - c =1
\(a^b=1\)
In order to make RHS =1, b has to be zero
so
\(a^0 = 1\)
but, still we don't know the unique value of "a". Hence Insufficient

Statement 2 - b≠0
\(a^b=c\)
\(a^b=c\)
We only know this that b is not Zero, but we don't know the value of "a". Hence insufficient

Statement 1 & 2 - c =1 & b≠0
\(a^b=c\)
\(a^b=1\)
We only know this that b is not Zero, but we don't know the value of "a".
1st Scenario- a , & b could 1 & 1 respectively to give c = 1
2nd Scenario- a , & b could -1 & 2 respectively to give c = 1

Hence insufficient
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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New post 27 Jun 2017, 02:28
elegantm Thanks for the explanation. How did I miss it!! :roll: :roll:
I missed the point that we could also take -1^2 or -1^4 etc examples like that.
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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New post 27 Jun 2017, 03:02
idinuv wrote:
\(a^b=c\)

If a, b and c are integers, what is the value of a?

(1) c=1

(2) b≠0


Given : a, b and c are integers
DS : a^b = c

Option 1 : c=1
a^b = 1, b = 0 then in that case a can assume any value.

NOT SUFFICIENT ...

Option 2: a^b = c b=/=0 .. This doesn't give us much idea about a.

Combined :
a^b = 1 and b=/=0
So a =1, b=1,2,3,4,...............
a=-1, b = 2,4,6,8,...........

So even combined options don't give one single value of a

Hence E is correct.
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Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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