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# If a and b are positive integers and a^3b^2 = 72, then a + b =

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Re: If a and b are positive integers and a^3b^2 = 72, then a + b = [#permalink]
Bunuel wrote:
If a and b are positive integers and $$a^3b^2 = 72$$, then a + b =

(A) 36

(B) 17

(C) 8

(D) 6

(E) 5

IMO E 72=2^3*3^2 so a=2 and b=3 and 3+2=5
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Re: If a and b are positive integers and a^3b^2 = 72, then a + b = [#permalink]
Bunuel wrote:
If a and b are positive integers and $$a^3b^2 = 72$$, then a + b =

(A) 36

(B) 17

(C) 8

(D) 6

(E) 5

Breaking 72 into prime factors we have:

72 = 3^2 x 2^3

Since a and b are positive integers, (a^3)(b^2) = (2^3)(3^2) is satisfied only when a = 2 and b = 3. Thus, a + b = 5.