Bunuel wrote:

If a, b and c are distinct positive integers, what is the value of (a + b + c)?

(1) \(2^{(2a+c)} + 3^b = 91\)

(2) \(2^{(a+2b)} + 3^{(\frac{c}{4})} = 13\)

(1)

\(2^{(2a+c)} + 3^b = 91\)

91 can only be 64 + 27

2a+c = 6 and b=3

now (a,b,c) can only be (1,3,4) (distinct positive integers)

Sufficient

(2)

\(2^{(a+2b)} + 3^{(\frac{c}{4})} = 13\)

13 can only be 4+9

c/4 = 2

c=8

a+2b = 2 (not possible) cannot identify the value of a+b as b or a cannot be 0

Not sufficient

A

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