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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: 51233
If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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21 Feb 2018, 22:09
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:50) correct 8% (01:14) wrong based on 81 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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Senior Manager
Joined: 07 Jul 2012
Posts: 377
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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21 Feb 2018, 22:14
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

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Joined: 26 Mar 2013
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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, 02:07
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

Manager
Joined: 23 Sep 2016
Posts: 216
Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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22 Feb 2018, 23:30
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
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If a and b are positive integers and a^3b^2 = 72, then a + b =  [#permalink]

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26 Feb 2018, 09:41
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.

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Re: If a and b are positive integers and a^3b^2 = 72, then a + b = &nbs [#permalink] 26 Feb 2018, 09:41
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