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

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Intern
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If a and b are distinct integers and a^b = b^a, how many  [#permalink]

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New post 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?
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If a and b are distinct integers and a^b = b^a, how many  [#permalink]

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New post 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,

Additionally, n/0 = not defined
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Re: If a and b are distinct integers and a^b = b^a, how many  [#permalink]

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New post 30 Oct 2018, 02:59
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Re: If a and b are distinct integers and a^b = b^a, how many   [#permalink] 30 Oct 2018, 02:59

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