Jul 16 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, July 16th at 8 pm EDT Jul 16 03:00 PM PDT  04:00 PM PDT Join a free live webinar and find out which skills will get you to the top, and what you can do to develop them. Save your spot today! Tuesday, July 16th at 3 pm PST Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 89
GMAT Date: 08082011

If A and B are nonzero integers, is A^B an integer? (1) B^A
[#permalink]
Show Tags
28 Apr 2011, 18:15
Question Stats:
46% (02:09) correct 54% (01:50) wrong based on 281 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.
Official Answer and Stats are available only to registered users. Register/ Login.



Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 950

Re: Is a^b an integer
[#permalink]
Show Tags
28 Apr 2011, 20:45
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.



Intern
Joined: 27 Apr 2011
Posts: 36
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, 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.



Retired Moderator
Joined: 16 Nov 2010
Posts: 1360
Location: United States (IN)
Concentration: Strategy, Technology

Re: Is a^b an integer
[#permalink]
Show Tags
28 Apr 2011, 23:21
(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
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 14 Jan 2015
Posts: 4
Location: United States
Concentration: International Business, Marketing
GPA: 3

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



CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
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, 11:20
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.



Current Student
Joined: 12 Aug 2015
Posts: 2609

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



Retired Moderator
Joined: 18 Sep 2014
Posts: 1100
Location: India

If A and B are nonzero integers, is A^B an integer? (1) B^A
[#permalink]
Show Tags
08 Apr 2016, 06:10
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



Manager
Joined: 04 Apr 2015
Posts: 104

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



CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
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, 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.



Manager
Joined: 26 Dec 2015
Posts: 246
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, 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 problemELIMINATE 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 problemELIMINATE BBetween 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 = EKudos please if you find this helpful



NonHuman User
Joined: 09 Sep 2013
Posts: 11662

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




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






