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

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Intern
Joined: 21 Mar 2013
Posts: 38
GMAT Date: 03-20-2014
a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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07 Mar 2014, 01:33
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Difficulty:

55% (hard)

Question Stats:

51% (01:05) correct 49% (00:56) wrong based on 240 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: a^b=c If a, b and c are integers, what is the value of a?  [#permalink]

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07 Mar 2014, 01:38
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.

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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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07 Mar 2014, 01:55
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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27 Jun 2017, 03:20
_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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27 Jun 2017, 03:28
elegantm Thanks for the explanation. How did I miss it!!
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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27 Jun 2017, 04:02
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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21 Nov 2019, 07:11
idinuv wrote:
$$a^b=c$$

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

(1) c=1

(2) b≠0

(1) c=1 insufic
$$(a,b)=(1,any):1^{any}=1$$
$$(a,b)=(any,0):(any)^0=1$$

(2) b≠0 insufic

(1&2) insufic
$$(a,b)=(1,2):1^{2}=1$$
$$(a,b)=(-1,2):(-1))^{2}=1$$

Ans (E)
Re: a^b=c If a, b and c are integers, what is the value of a?   [#permalink] 21 Nov 2019, 07:11
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# a^b=c If a, b and c are integers, what is the value of a?

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