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

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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21 Feb 2018, 23:09
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Difficulty:

5% (low)

Question Stats:

89% (00:50) correct 11% (01:03) wrong based on 86 sessions

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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

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Posts: 367
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Concentration: Finance, Accounting
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Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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21 Feb 2018, 23:14
Factors of 72 are: $$2^3$$*$$3^2$$

So $$a^3$$$$b^2$$= $$2^3$$*$$3^2$$

So a= 2 and b=3

a + b= 5

Answer: E.
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Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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22 Feb 2018, 03:07
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

Prime factorization

$$a^3b^2 = 72$$ = $$2^3 3^2$$

a +b = 2+3 =5

Answer: E
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Joined: 23 Sep 2016
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Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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23 Feb 2018, 00:30
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]

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26 Feb 2018, 10:41
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.

Answer: E
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Re: If a and b are positive integers and a^3b^2 = 72, then a + b =   [#permalink] 26 Feb 2018, 10:41
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# If a and b are positive integers and a^3b^2 = 72, then a + b =

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