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# If A and B are nonzero integers, is A^B an integer? (1) B^A

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Manager
Joined: 03 Aug 2010
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GMAT Date: 08-08-2011
If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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28 Apr 2011, 18:15
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Question Stats:

46% (02:09) correct 54% (01:50) wrong based on 281 sessions

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If A and B are nonzero integers, is $$A^B$$ an integer?

(1) $$B^A$$ is negative
(2) $$A^B$$ is negative

Please explain the most efficient way to attack this question.
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Re: Is a^b an integer  [#permalink]

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28 Apr 2011, 20:45
1
2
a B^A <0 => B is essentially negative and A is Odd number. For B=A = -1 and for B=-1 and A=3 the values are different.
b A^B <0 => A is essentially negative and B is an Odd number. For similar values the equation gives different outcomes.

for a+b, A=B= -1 and for A= -3 and B= -1 the values are different.Hence IMO E.

Under such condition we have to always check for A=B values and A> or <B values.
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Re: Is a^b an integer  [#permalink]

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28 Apr 2011, 20:48
The answer is E i guess

A. B^A is <0
that means that B<0 and A is odd
case 1 :
So consider A = -1 B is 3

(-1)^3 = -1 YES

Consider A=-3 and B=-2

(-3)^-2 = -1/9 NO Insufficient

B. A^B <0 A < 0 B is odd

so this is also insufficient as we can use the same values as above

combining both A,B <0 and A,B Odd numbers

so the case fails whenever A is -1 since -1 is also an odd number

E is the answer.
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Re: Is a^b an integer  [#permalink]

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28 Apr 2011, 23:21
1
1
(1)
B^A = -ve

So B is -ve and A is odd (-ve or +ve)

(1) is insufficient, because if A is -ve, B^A may not be an integer.

(2)
A^B is -ve

So A is -ve and B is odd ( +ve or -ve)

(2) is insufficient as well

(1) and (2) say :

A and B are -ve and odd

So A^B may/may not be an integer

(-1)^-1 = -1

(-3)^-3 = not an integer

Answer - E
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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19 Jan 2015, 05:40
I guess positivity and negativity doesn't say much about a number being integer or a decimal. So you should go for E.
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If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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08 Mar 2016, 11:20
2
Chiragjordan wrote:
Hey MIKE Can you help with this one..

attempted twice.. got it wrong both times..
I choose A both the times...

Whenever you are quoting a user, use "@"before the correct username. I believe you want to ask inputs from mikemcgarry from Magoosh.

As for this question, it hinges on the observation that $$A^B$$ will be <0 when A < 0 for B=odd. Thus for $$A^B$$ to be an integer ---> A =$$\pm$$ 1 and B can be any odd integer ($$\neq$$ 0). Analyse the given statements in light of this information.

Per statement 1, $$B^A$$< 0 ---> The only possible case is B < 0 and A= odd. If B = -1, A = any power, you get a yes to the question asked but if B = -3 and A = 1, you get -1/3 = no for the question asked. Not sufficient.

Per statement 2, $$A^B$$ < 0 ---> The only possible case is A<0 and B = odd. Same logic as that for statement 1. Not sufficient.

Combining, you get that A = B = odd negative integer and as such you get a yes if A=B=-1 but you get a NO for A=-3 and B = -1.

Hence E is thus the correct answer.

Hope this helps.
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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13 Mar 2016, 22:46
Engr2012 wrote:
Chiragjordan wrote:
Hey MIKE Can you help with this one..

attempted twice.. got it wrong both times..
I choose A both the times...

Whenever you are quoting a user, use "@"before the correct username. I believe you want to ask inputs from mikemcgarry from Magoosh.

As for this question, it hinges on the observation that $$A^B$$ will be <0 when A < 0 for whatever value of B. Thus for $$A^B$$ to be an integer ---> A =$$\pm$$ 1 and B can be any integer ($$\neq$$ 0). Analyse the given statements in light of this information.

Per statement 1, $$B^A$$< 0 ---> The only possible case is B < 0 and A= odd. If B = -1, A = any power, you get a yes to the question asked but if B = -3 and A = 1, you get -1/3 = no for the question asked. Not sufficient.

Per statement 2, $$A^B$$ < 0 ---> The only possible case is A<0 and B = odd. Same logic as that for statement 1. Not sufficient.

Combining, you get that A = B = odd negative integer and as such you get a yes if A=B=-1 but you get a NO for A=-3 and B = -1.

Hence E is thus the correct answer.

Hope this helps.

Thank you so much for the explanation
here is what i think i made the mistake=>
In the first case i neglected A being 1 or -1
So combining the two statements => A can be -1 B=-21=> integer
and A= anything but -1 ,B=anything => non integer..
Is this understanding correct?
regards
Also whats the point of tagging the name when they only respond when they want else they DON'T..
Regards
Stone Cold Steve Austin
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If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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08 Apr 2016, 06:10
3
1
If $$a$$ and $$b$$ are nonzero integers, is $$a^b$$ an integer?

(1) $$b^a$$ is negative

This can be true when $$b$$ is negative integer(odd or even) and $$a$$ is odd(negative or postive)
If $$a=1$$, then all cases of $$a^b$$ is an integer
If $$a=3$$, None of the cases give an integer for $$a^b$$

Not sufficient

(2) $$a^b$$ is negative

Negative can be an integer or decimal or real number as well.

for $$b=1$$ & $$a=-3,-2$$
we have some values of $$a^b$$ as integer and some are not integer(decimal) values.

Thus insufficient.

Combining 1 and 2
we get both a and b as odd and negative integers
Try the intended expression $$a^b$$ with values (a,b) as (-1,-3) and (-3,-1).
we get both integer and non integer values -3 and -0.333.
Thus combining both the statements is also insufficient.

Ans E
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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08 Apr 2016, 14:37
I cant understand why people are assuming that both premise A or B(eg B^A i negative) talking about integers

Option A says B^A is negative, it doesnt say that B^A is neg interger so why all are assuming it to be.

Answer should be A since we can find out the sign of B will be neg so A^B will never be an integer.

Statement 1 is suff
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If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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08 Apr 2016, 16:38
varundixitmro2512 wrote:
I cant understand why people are assuming that both premise A or B(eg B^A i negative) talking about integers

Option A says B^A is negative, it doesnt say that B^A is neg interger so why all are assuming it to be.

Answer should be A since we can find out the sign of B will be neg so A^B will never be an integer.

Statement 1 is suff

No one is ASSUMING anything. Refer to the solution mcp.php?i=main&mode=post_details&f=141&p=1656135 that clearly uses 2 distinct cases. Alternately, look at the following 2 cases:

Case 1: B=-1 and A = 3 ---> B^A < 0 and A^B $$\neq$$ integer but

Case 2: B=-2 and A = -1 ---> B^A < 0 and A^B = integer

Thus you clearly get 2 different answers for the question asked --> Is A^B an integer ---> Thus this statement is NOT sufficient.

Hope this helps.
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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02 May 2017, 16:31
If a and b are nonzero integers, is $$a^{b}$$ an integer?

(1) $$b^{a}$$ is negative
(2) $$a^{b}$$ is negative

Please explain the most efficient way to attack this question.

The KEY here is to pick numbers. Let's go:

1) $$b^{a}$$ is negative
- We know from this equation that a=odd AND b=negative
-- TEST VALUES:
> $$-3^{3}$$ = -27. INTEGER.
> $$-3^{-3}$$ = $$\frac{-1}{27}$$. NOT AN INTEGER.
* KEY: b is negative, but a is just "odd"...this means a can be positive or negative, and this differentiator makes or breaks the problem

ELIMINATE A&D

$$a^{b}$$ is negative
- We know from this equation that a=negative AND b=odd
-- TEST VALUES:
> $$-5^{3}$$ = -125. INTEGER.
> $$-5^{-3}$$ = $$\frac{-1}{125}$$. NOT AN INTEGER.
* KEY: a is negative, but b is just "odd"...this means b can be positive or negative, and this differentiator makes or breaks the problem

ELIMINATE B

Between C&E
- We know from BOTH equations that BOTH a&b need to be ODD AND NEGATIVE.
-- TEST VALUES:
> $$-3^{-3}$$ = $$\frac{-1}{27}$$. NOT AN INTEGER.
> $$-1^{-3}$$ = 1. INTEGER.

HENCE, CORRECT ANSWER = E

Kudos please if you find this helpful
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A  [#permalink]

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08 Jan 2019, 19:32
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Re: If A and B are nonzero integers, is A^B an integer? (1) B^A   [#permalink] 08 Jan 2019, 19:32
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