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# M13-32

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Math Expert
Joined: 02 Sep 2009
Posts: 50613

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15 Sep 2014, 23:50
1
2
00:00

Difficulty:

85% (hard)

Question Stats:

45% (00:45) correct 55% (01:23) wrong based on 85 sessions

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Is $$a^b \gt b^a$$ ?

(1) $$a \gt b \gt 1$$

(2) $$a = b + 1$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50613

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15 Sep 2014, 23:50
Official Solution:

Statements (1) and (2) combined are insufficient. Consider:

$$a = 3$$, $$b = 2$$. $$a^b = 3^2 = 9 \gt b^a = 2^3 = 8$$. The answer is "yes".

$$a = 4$$, $$b = 3$$. $$a^b = 4^3 = 64 \lt b^a = 3^4 = 81$$. The answer is "no".

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Intern
Joined: 01 Feb 2017
Posts: 3
Location: India
GMAT 1: 690 Q47 V37
GPA: 4

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08 Apr 2018, 21:26
For values less than zero even both the statements are not enough.
check with values less than zero
Intern
Joined: 02 Feb 2018
Posts: 17

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02 Nov 2018, 09:30
You can save a lot of time on this one when you start by picking numbers that satisfy both statements at the same time as Bunuel did.. I wonder if this should be the default state when facing DS questions where picking numbers is obviously the best way to go - any advice on this? Or what specific signaled you in this question that this is the best strategy?
Re: M13-32 &nbs [#permalink] 02 Nov 2018, 09:30
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# M13-32

Moderators: chetan2u, Bunuel

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