Lets come straight to combining both statements (A and B can independently ruled out clearly.

We suggest to begin by using simplest of the values-
Lets say y=2 (so that 2 in the 1/2 can be cancelled) and h=5
=> 1/2 * 2* 5 = 5 and less than 20.
 But if we take base as x with x=6 and h=7 then area =1/2 * 6*7 =21 and is greater than 20. (Insufficient)
Thus (option e)

Even without plugging in, with adequate practice and exposure to such questions, you can observe and be able to mark (E) by realizing that that the situation is NOT hinting at Diophantine equation, the situation is an inequation and hence plugged in values have a high probability of disproving the combination of st(1) and st(2). 
E would be the "best fit" answer choice under a time crunch. 
You must plug in and check when you have 2-2.5 min for such questions.