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If a and b are non -zero distinct integers, what is the value of a + b

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mangamma
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If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   Updated on: 30 May 2019, 04:41
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If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1/243

(2) a^b = a
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Official Answer
E

Originally posted by mangamma on 19 Apr 2019, 09:13.
Last edited by mangamma on 30 May 2019, 04:41, edited 1 time in total.
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chetan2u
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   19 Apr 2019, 22:35
Expert Reply
mangamma wrote:
If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1243

(2) a^b = a



Of course statement I has some error..
Right side is not a multiple of 3, while left hand side is a qty to power of 3..
I assume it should have been \(\frac{1}{243}\)

So we are looking for a+b...

(1) \((3^a)^b=\frac{1}{243}=3^{-5}\)
So ab=-5...so ab could be -1*5 or 1*(-5). Thus a+b could be 4 or -4.
Insufficient

(2) \(a^b=a\).
We do not know the exact value of a and b.
Insufficient

Combined..
ab=-5 and \(a^b=a\)..
When a=-5 and b=1...\(-5^1=-5\) and a+b=-5+1=-4..
But when a=-1 and b=5..\((-1)^5=-1\) and a+b=-1+5=4..
Thus a+b could be -4 or 4
Insufficient

E..

mangamma please check statement I.
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   30 May 2019, 04:41
chetan2u wrote:
mangamma wrote:
If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1243

(2) a^b = a



Of course statement I has some error..
Right side is not a multiple of 3, while left hand side is a qty to power of 3..
I assume it should have been \(\frac{1}{243}\)

So we are looking for a+b...

(1) \((3^a)^b=\frac{1}{243}=3^{-5}\)
So ab=-5...so ab could be -1*5 or 1*(-5). Thus a+b could be 4 or -4.
Insufficient

(2) \(a^b=a\).
We do not know the exact value of a and b.
Insufficient

Combined..
ab=-5 and \(a^b=a\)..
When a=-5 and b=1...\(-5^1=-5\) and a+b=-5+1=-4..
But when a=-1 and b=5..\((-1)^5=-1\) and a+b=-1+5=4..
Thus a+b could be -4 or 4
Insufficient

E..

mangamma please check statement I.


Edited. thank you
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aviejay
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   03 Jun 2019, 09:28
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mangamma wrote:
chetan2u wrote:
mangamma wrote:
If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1243

(2) a^b = a



Of course statement I has some error..
Right side is not a multiple of 3, while left hand side is a qty to power of 3..
I assume it should have been \(\frac{1}{243}\)

So we are looking for a+b...

(1) \((3^a)^b=\frac{1}{243}=3^{-5}\)
So ab=-5...so ab could be -1*5 or 1*(-5). Thus a+b could be 4 or -4.
Insufficient

(2) \(a^b=a\).
We do not know the exact value of a and b.
Insufficient

Combined..
ab=-5 and \(a^b=a\)..
When a=-5 and b=1...\(-5^1=-5\) and a+b=-5+1=-4..
But when a=-1 and b=5..\((-1)^5=-1\) and a+b=-1+5=4..
Thus a+b could be -4 or 4
Insufficient

E..

mangamma please check statement I.


Edited. thank you



Hi,

From second statement, we can deduce the value of b to be either 0 or 1.

1^0=1
(Any number) ^ 1= same number

Clubbing with A, we get A=-5.

Answer should be C.please correct me where am i going wrong.
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Neha2050
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   09 Jun 2019, 11:43
mangamma wrote:
If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1/243

(2) a^b = a


a^b =a^1=a
hence b=1
combing both
b=1 and a=-5
pls correct and expliain how is this wrong by quoting any other case where a^b=a is not possible for b=1
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   09 Jun 2019, 12:19
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You missed two cases, when a=1 and b can have any integral value and when a=-1 and b has odd integral value. Hence you will have 3 solutions when you combine the equations.
(a,b)=(-5,1) or (1,-5) or (-1,5)
Hence we can have 2 possible values of a+b that is 4 or -4
Hence insufficient

Neha2050 wrote:
mangamma wrote:
If a and b are non -zero distinct integers, what is the value of a + b?

(1) (3^a)^b=1/243

(2) a^b = a


a^b =a^1=a
hence b=1
combing both
b=1 and a=-5
pls correct and expliain how is this wrong by quoting any other case where a^b=a is not possible for b=1


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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   30 Nov 2020, 16:54
Ya I still don't see why the answer is E like others have stated.
The possibilities for a and b are
a = -1, b = 5
a = 5, b = -1
a = -5, b = 1

We know that a^b = a^1 <-- b = 1. b cannot equal anything else given statement 2.

May someone explain further?
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink] New post   20 Nov 2023, 01:23
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Re: If a and b are non -zero distinct integers, what is the value of a + b [#permalink]
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