It is currently 17 Dec 2017, 19:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 105

Kudos [?]: 101 [1], given: 63

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

### Show Tags

28 Apr 2011, 17:15
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

45% (01:29) correct 55% (01:29) wrong based on 239 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA

Kudos [?]: 101 [1], given: 63

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1267

Kudos [?]: 292 [0], given: 10

Re: Is a^b an integer [#permalink]

### Show Tags

28 Apr 2011, 19:45
1
This post was
BOOKMARKED
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.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 292 [0], given: 10

Intern
Joined: 27 Apr 2011
Posts: 36

Kudos [?]: 18 [0], given: 7

Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 660 Q47 V33
GMAT 2: 730 Q50 V40
GPA: 3.37
WE: Programming (Computer Software)
Re: Is a^b an integer [#permalink]

### Show Tags

28 Apr 2011, 19:48
1
This post was
BOOKMARKED
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

Kudos [?]: 18 [0], given: 7

TOEFL Forum Moderator
Joined: 16 Nov 2010
Posts: 1589

Kudos [?]: 608 [1], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Re: Is a^b an integer [#permalink]

### Show Tags

28 Apr 2011, 22:21
1
KUDOS
1
This post was
BOOKMARKED
(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

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 608 [1], given: 40

Non-Human User
Joined: 09 Sep 2013
Posts: 14796

Kudos [?]: 288 [0], given: 0

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

### Show Tags

23 Dec 2014, 15:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 288 [0], given: 0

Intern
Joined: 14 Jan 2015
Posts: 4

Kudos [?]: 5 [0], given: 3

Location: United States
GPA: 3
Re: If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

19 Jan 2015, 04:40
I guess positivity and negativity doesn't say much about a number being integer or a decimal. So you should go for E.

Kudos [?]: 5 [0], given: 3

Non-Human User
Joined: 09 Sep 2013
Posts: 14796

Kudos [?]: 288 [0], given: 0

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

### Show Tags

25 Feb 2016, 23:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 288 [0], given: 0

Retired Moderator
Joined: 12 Aug 2015
Posts: 2227

Kudos [?]: 914 [0], given: 616

GRE 1: 323 Q169 V154
Re: If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

08 Mar 2016, 10:03
Hey MIKE Can you help with this one..

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

Give me a hell yeah ...!!!!!

Kudos [?]: 914 [0], given: 616

Current Student
Joined: 20 Mar 2014
Posts: 2673

Kudos [?]: 1791 [2], given: 797

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

08 Mar 2016, 10:20
2
KUDOS
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.

Kudos [?]: 1791 [2], given: 797

Retired Moderator
Joined: 12 Aug 2015
Posts: 2227

Kudos [?]: 914 [0], given: 616

GRE 1: 323 Q169 V154
Re: If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

13 Mar 2016, 21:46
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
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 914 [0], given: 616

Retired Moderator
Joined: 18 Sep 2014
Posts: 1199

Kudos [?]: 910 [3], given: 75

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

### Show Tags

08 Apr 2016, 05:10
3
KUDOS
1
This post was
BOOKMARKED
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
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.

My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773

Kudos [?]: 910 [3], given: 75

Manager
Joined: 04 Apr 2015
Posts: 104

Kudos [?]: 30 [0], given: 3959

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

### Show Tags

08 Apr 2016, 13:37
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

Kudos [?]: 30 [0], given: 3959

Current Student
Joined: 20 Mar 2014
Posts: 2673

Kudos [?]: 1791 [0], given: 797

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

08 Apr 2016, 15:38
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.

Kudos [?]: 1791 [0], given: 797

Senior Manager
Joined: 26 Dec 2015
Posts: 262

Kudos [?]: 59 [0], given: 1

Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: If A and B are nonzero integers, is A^B an integer? (1) B^A [#permalink]

### Show Tags

02 May 2017, 15:31
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.

Kudos [?]: 59 [0], given: 1

Re: If A and B are nonzero integers, is A^B an integer? (1) B^A   [#permalink] 02 May 2017, 15:31
Display posts from previous: Sort by