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

Question

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

varun4s · Answer

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.

Mo2men · Answer

Prime factorization

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

a +b = 2+3 =5

Answer: E

rishabhmishra · Answer

IMO E 72=2^3*3^2 so a=2 and b=3 and 3+2=5

JeffTargetTestPrep · Answer

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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