Baldini wrote: 1.
(5+6)+2=5+(6+2) possibility is + (addition)
(5*6)*2=5*(6*2) possibility is * (multiplication)
It can not be division or subtraction.

INSUFF

2.
2+0=2 possibility is + (addition)
2*0=/2 can not be * (multiplication)
2-0=2 possibility is - (subtraction)
2/0=/2 can not be / (division)

INSUFF

Together we get addition as the answer.

Baldini,

You don’t really need to prove that the symbol must be an addition. All you need to do is conclusively prove that the equation in the question stem is true or false (i.e. by answering a definite yes, or no).

Before looking at the statements, first look at the question stem:

Is (5∆6) ∆2 = 5∆(6∆2) ? Under what circumstances will be will this be true?

If ∆ = addition, the equation is satisfied
If ∆ = multiplication, the equation is satisfied
If ∆ = substraction, the equation is NOT satisfied
If ∆ = division, the equation is NOT satisfied

Statement 1:
As you had worked out, ∆ could be either addition or multiplication. We don't really care which of these two ∆ really is, all we care about is that we can now conclusively say that the equation is true.

Statement 2:
∆ can be addition, or substraction. Both possibilities contradict the answer to the question stem. Insufficient.

Hope that helps.

-BM-

we need to answer the question in the stimulus: whether LHS=RHS

1) the symbol can be multiplication or addition.
if we apply either to the symbol in the stimulus we get LHS=RHS

if addition=>(5+6)+2=5+(6+2)
if multiplication=>(5*6)*2=5*(6*2)

so both addition and multiplication works. sufficient

2) the symbol can be addition or subtraction.
if addition: (5+6)+2=5+(6+2)
if subtraction: (5-6)-2=-3 not equal to 5-(6-2)=1
not sufficient

hence A