Question: Is x less than 20?

(St 1): The sum of x and y is less than 20.

(St 2): y is less than 20.

From GMAT prep software. OA is E. My problem is NOT seeing why E is correct. I can easily pick numbers and prove why that is so. The thing that has me baffled is why a straightforward algebraic approach doesn't work. I always thought you could add inequalities as long as the ineq symbol was pointed in the same direction. Also, if you look at the thread for the question "Is xy<20?" you'll see a suggestion that this is the case (from Ron P).

So, when I saw this question, I quickly wrote the question as "Is x<20." I then wrote statement 1 as "x+y < 20" and I wrote statement 2 as "y< 20." After quickly eliminating S1 & S2, I subtracted S2 from S1 and I got x < 0. If x<0, then x MUST BE less than 20. So I picked C and moved on, thinking I'd cracked it with no sweat. Where did I go wrong? What's the underlying principle I'm missing? I thought I'd shredded this one quickly and was surprised to see the result. It's got me questioning a tool I thought was a basic one for inequalities. Many thanks.