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# If a and b are distinct integers and a^b = b^a, how many

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Intern
Joined: 09 Jul 2015
Posts: 9
Location: India
WE: Marketing (Other)
If a and b are distinct integers and a^b = b^a, how many  [#permalink]

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19 Aug 2015, 07:05
VeritasPrepKarishma wrote:
A 700-level question for the GMAT committed souls studying over the weekend.

If a and b are distinct integers and $$a^b = b^a$$, how many solutions does the ordered pair (a, b) have?

(A) None
(B) 1
(C) 2
(D) 4
(E) Infinite

Hint: Use logic, not Math. Look for patterns.

Why is $$0^1$$ and $$1^0$$ not applicable? Aren't they both = 1?
CEO
Joined: 20 Mar 2014
Posts: 2561
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 distinct integers and a^b = b^a, how many  [#permalink]

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19 Aug 2015, 07:26
nitika231 wrote:
VeritasPrepKarishma wrote:
A 700-level question for the GMAT committed souls studying over the weekend.

If a and b are distinct integers and $$a^b = b^a$$, how many solutions does the ordered pair (a, b) have?

(A) None
(B) 1
(C) 2
(D) 4
(E) Infinite

Hint: Use logic, not Math. Look for patterns.

Why is $$0^1$$ and $$1^0$$ not applicable? Aren't they both = 1?

for any 'n' $$\in$$integer

$$0^n$$ = 0 , while

$$n^0$$ = 1,

Intern
Joined: 17 Jun 2019
Posts: 9
Location: United States
GPA: 3.92
Re: If a and b are distinct integers and a^b = b^a, how many  [#permalink]

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18 Aug 2019, 11:54
Re: If a and b are distinct integers and a^b = b^a, how many   [#permalink] 18 Aug 2019, 11:54

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