Is 3x + y = 333? (1) x - y = 33 (2) x/y = 1/3

Here are the first two things I noticed.

First, if you use both statements, you can find the exact values of x and y. Therefore, the answer can't possibly be E. In this situation you should also be very skeptical of C. C might be the right answer, but it also seems 'too easy' - maybe they're trying to trick you.

Second, I wonder if this problem will test Number Properties. Just about the only thing I know about the number 333 is that it's definitely divisible by 3. Also, we're multiplying x by 3. Maybe there's something to do with divisibility here?

Anyways, let's go on to the statements!

Statement 1: x - y = 33, or x = y + 33. Let's plug it in to the question:

Is 3x + y = 333?

Is 3(y + 33) + y = 333?

Is y = (some number)?

Without the value of y, you don't know whether the answer is "yes" or "no", so this is insufficient.

Statement 2: x/y = 1/3, or 3x = y. Let's plug it into the question:

Is 3x + y = 333?

Is 2y = 333?

Is y = (some number)?

Again, without the value of y, you don't know, so this is insufficient. Note that we're keeping the 'is' and the question mark, to remind us that this is a QUESTION, not something we know for sure!

Statements 1 and 2 together: You can definitely find the values of x and y, since you have two statements that give you different equations relating the two variables to each other.

x = y + 33
3x = y

x = 3x + 33
-2x = 33
x = -16.5

y = 3(-16.5) = -49.5

The answer is definitely "No," since 3(-16.5) + (-49.5) certainly won't be equal to 333 (because it's negative). Because the answer is a definite No, the answer to the problem is C. However, note that this is extremely unusual for a Data Sufficiency problem. This does happen in official problems (a definite 'no' answer) but it's very, very rare, and it makes me suspect that this problem may be from a questionable source. Be cautious!