GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Feb 2020, 05:26

### 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

# Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61280
Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

08 Oct 2019, 19:55
00:00

Difficulty:

65% (hard)

Question Stats:

48% (02:22) correct 52% (01:44) wrong based on 25 sessions

### HideShow timer Statistics

Competition Mode Question

Is $$A^B > B^A$$?

(1) $$A^A > A^B$$

(2) $$B^A > B^B$$

_________________
Director
Joined: 07 Mar 2019
Posts: 685
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

08 Oct 2019, 20:38
Is $$A^B>B^A$$?

Only if it is known A > B or A < B, a concrete YES/NO answer can be found.

(1) $$A^A > A^B$$

Since base are same, A > B. YES
SUFFICIENT.

(2) $$B^A>B^B$$

Since base are same, A > B. YES
SUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
CR Forum Moderator
Joined: 18 May 2019
Posts: 706
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

08 Oct 2019, 21:59
1
Is A^B > B^A?

Statement 1: A^A > A^B
Insufficient because if A=2, and B=1, satisfying the condition in statement 1, we have A^B (2) > B^A (1)
however, if A=-2, and B=-3, satisfying the condition in statement 1 as well, we have A^B (-1/8) < B^A (1/9).

Statement 2: B^A > B^B.
Insufficient because if A=3, B=2, satisfying the condition in statement 2, we A^B (9) > B^A (8)
however, if A=-2, and B=-3, satisfying the condition in statement 2, we have A^B (-1/8) < B^A (1/9)

Statement 1 + Statement 2:
Both statements are still insufficient.
This is because if A=3, and B=2, satisfying both statements, A^B (9) > B^A (8)
however, if A=-2, and B=-3, also satisfying both statements, A^B (-1/8) < B^A (1/9).

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5924
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

Updated on: 10 Oct 2019, 05:18
#1
A^A>B^A
base is common so A>B
for all integer values +/-ve we get A^B>B^A we get yes/no ; insufficient
#2
B^A>B^B
again base is common so A>B
hence for all integer values +/-ve we get A^B>B^A we get yes/no ; insufficient
IMO E

Is A^B>B^A

(1) A^A>A^B
(2) B^A>B^B

Originally posted by Archit3110 on 09 Oct 2019, 02:34.
Last edited by Archit3110 on 10 Oct 2019, 05:18, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 8261
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

09 Oct 2019, 03:07
1
1
Is $$A^B > B^A$$?
All those who forget that the values of A and B can be anything that is negative, positive, fraction or integers will go wrong by marking D.

(1) $$A^A > A^B$$
A=3 and B=2...Yes
A=4 and B=3...No
A=-2 and B=-3..No

(2) $$B^A > B^B$$
A=3 and B=2...Yes
A=-2 and B=-3..No

Combined..
A=3 and B=2...Yes
A=-2 and B=-3..No

E
_________________
VP
Joined: 24 Nov 2016
Posts: 1204
Location: United States
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

09 Oct 2019, 04:03
1
Quote:
Is A^B>B^A?

(1) $$A^A>A^B$$
(2) $$B^A>B^B$$

case: a… b… a^a… b^b… a^b… b^a… condition y/n:
I.…: 1… -1… 1… -1… 1… -1… 1>-1? yes
II.…: -2…-3…1/4…-1/27…-1/8…1/9…-1/8>1/9? no
III.…: 2… -3…4……-1/27…1/8…1/9…1/8>1/8? yes

(1) $$A^A>A^B$$: all cases are valid, insufic.
(2) $$B^A>B^B$$: case II. and III. are valid, insufic.

(1&2): case II. and III. are valid, insufic.

Intern
Joined: 27 Jan 2017
Posts: 33
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

09 Oct 2019, 05:09
1
(1) Shows that A > B
Using the above we can say...
If B is negative and A is positive and even B^A could be greater than A^B
If A and B are both positive integers A could be greater than B

Therefore 1 is NS

(2) Also Shows that A > B

Therefore 2 is NS

(1+2) Statements 1 and 2 could both be true
If B is negative and A is positive and even B^A could be greater than A^B
If A and B are both positive integers A could be greater than B

Therefore Answer must be (E) as 1 and 2 combined are insufficient
Director
Joined: 25 Jul 2018
Posts: 544
Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B  [#permalink]

### Show Tags

09 Oct 2019, 15:56
1
Is $$A^{B}>B^{A}$$ ?

Statement1: $$A^{A}>A^{B}$$

if the base of exponent is greater than 1(A>1), then
--> A>B.
-------
if A=3 and B=2, then 9 > 8 (YES)
if A=5 and B=2, then 25 >32} (NO)
Insufficient

Statement2: $$B^{A}>B^{B}$$

if the base of exponent is greater than 1(B>1), then
--> A>B.
-------
if A=3 and B=2, then 9 > 8 (YES)
if A=5 and B=2, then 25 >32} (NO)
Insufficient

Taken together 1&2, Clearly insufficient.

Re: Is A^B > B^A? (1) A^A > A^B (2) B^A > B^B   [#permalink] 09 Oct 2019, 15:56
Display posts from previous: Sort by