Just as Kevin says. If we understand the concepts of false positives and false negatives, and recognize that this question can be construed as testing those concepts, then we can solve this question quickly. But you can still solve this question without knowing about these concepts formally.
I'll try to take a shot here.
The author's conclusion is:
Clearly, using this test, doctors can largely avoid unnecessary removals of the appendix without, however, performing any fewer necessary ones than before, since .......
The part in bold basically means that, with the test, they'll still perform the same number of necessary operations (as they used to). In other words, they'll catch people who have appendicits just as much as they used to.
To complete this argument we need to find some evidence that supports the conclusion (notice the keyword "since").
How can we support the conclusion that they'll catch just as many people who have appendicits as they used to?
Well, if the 2% error rate is exclusively due to the test saying you have appendicits when you don't (rather than not catching your appendicits), then the author's argument is supported (since the error rate without the test is 20%)...that's essentially what choice B says.
As gmatmachoman points out, we can also use the denial test to prove that choce B supports the argument:
If the 2% error rate were due to the test
not catching your appendicits, then the author's conclusion that the test would decrease the number of unnecessary operations is clearly weakened: the test would be decreasing the number of NECESSARY operations--clearly a bad outcome. Because the denial of choice B hurts the argument, choice B must be evidence that supports the argument.
Kaplan Teacher in Toronto