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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

Kudos [?]: 8 [0], given: 4

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?

Kudos [?]: 8 [0], given: 4

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1725 [0], given: 792

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,

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Kudos [?]: 1725 [0], given: 792

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Joined: 09 Sep 2013
Posts: 16636

Kudos [?]: 273 [0], given: 0

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

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28 Sep 2017, 21:20
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).

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Kudos [?]: 273 [0], given: 0

Re: If a and b are distinct integers and a^b = b^a, how many   [#permalink] 28 Sep 2017, 21:20

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