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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. _________________

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

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23 Dec 2014, 16:14

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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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26 Feb 2016, 00:46

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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

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Expert's post

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.

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

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

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This post received KUDOS

Expert's post

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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