Statement 1: x+y<20.
For most test-takers, the best approach here would be plugging in values. Plug in y=5, for example, and x can be 10. 10 is less than 20, so in this case the answer is yes. Plug in a negative number as well- if y=-5, x can be greater than 20 (22, for example, since 22+(-5) = 17). So the answer may also be 'no' - insufficient.
For those more algebra-oriented, subtract y from both sides: x+y<20 --> x<20-y. We have no data about y, so the statement is insufficient.
Statement 2: y<20.
This statement can be proven to be insufficient with the exact same plug in values as statement 1 (both y=5 and y=-5 satisfy 'y is less than 20'). y=5 and y=-5 lead to different answers, therefore the statement is insufficient.
Statement 1+2:
Again, same plug in values as before do the trick: y=5 & x=10: 'yes'; y=-5 & x=22: 'no'.
Correct answer is E.
Generally speaking, this entire question revolves around a single concept: if y is positive, adding it to x leads to an increase (thus if y is positive, x must be smaller than 20). On the other hand, If y is negative, adding it to x leads to a decrease (thus allowing x to be greater than 20). Either understand the logic, or keep lugging in until you're convinced.
Roy
Master GMAT
