In order to find the solution, you must determine what the "_" operator is.
From the stem, we're trying to find:
Is k o (l+m) = (k o l) + (k o m), for all numbers k.l, and m.
For "+". k + (l+m) = k + l + m.
Is this equal to (k + l) + (k + m) = k + l + k + m = 2k + l + k. NO. So, the equation will always fail if "o" is "+".
For "x". k x (l+m) = kl + km.
Is this equal to (k x l) + (k x m) = kl + km. YES. So, the equation will always succeed if "o" = "x".
Now because "_" can equal another operation, we must test the other two.
For "-". k - (l+m) = k - l - m.
Is this equal to (k - l) + (k - m) = k - l + k - m = 2k - l - m. NO.
For "/". k/(l+m).
Is this equal to (k/l) + (k/m) = (km - kl)/(lm) = [k(m-l)]/(lm). NO.
So for the equation to succeed, the operator must be "x".
(1) k o 1 is not equal to 1 o k for some numbers k.
You should be able to determine that this is true for "-" (subtraction) and "/" (division). So, we know "o" is either "-" or "/". Both cause the stem question to FAIL, so this is SUFFICIENT to answer the question (as we KNOW the answer will ALWAYS be NO).
(2) o represents subtraction.
As proven in our initial work, "-" causes the stem question to FAIL, so this is SUFFICIENT to answer the question (as we KNOW the answer will ALWAYS be NO).
Answer: D. Either statement, by itself, is Sufficient to answer the question.
