Bunuel wrote:

A, B, and C are three consecutive even integers (not necessarily in order). Which has the greatest value?

(1) A + B = C

(2) C is a positive number.

Let the three consecutive even integers be x, x+2 and x+4 (we dont know which one is A, which one is B and which one is C yet).

(1) A + B = C

Here three cases are possible:

Case I) x + x+2 = x+4 (here we have taken C to be x+4)

Solving this, we get x=2. And the three are 2, 4, 6. Largest value (6) is of x+4, which is C.

Case II) x + x+4 = x+2 (here we have taken C to be x+2)

Solving this, we get x=-2. And the three are -2, 0, 2. Largest value (2) is of x+4, which could be either A or B.

Case III) x+2 + x+4 = x (here we have taken C to be x)

Solving this, we get x=-6. And the three are -6, -4, -2. Largest value (-2) is of x+4, which could be either A or B.

So, as is clear from these three cases, largest value could be of A or B or C. So

not sufficient.

(2) C is a positive number. If the three integers are 2, 4, 6 (say) then C could be any one out of these three. We cant say which one has largest value. So

not sufficient.

Combining the two statements, if we look at all the three cases, there is only one case where C is positive. It is the first case, where the three integers are 2, 4, 6.

This means C = 6, and thus the largest.

Sufficient.

Hence

C answer