STRATEGY: As with all GRE Multiple Choice questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
At this point, we should typically give ourselves 15 to 20 seconds to identify a faster approach, but testing the answer choices will be incredibly easy, and I'm pretty sure I'll need to test 2 answer choices at most. So, I'll start testing the answer choices immediately.

We'll start with answer choice C - 41
There are 50 questions and total.
If the student correctly answered 41 questions, we know that the student incorrectly answered 9 questions.
Total score =41 - (2)(9) = 41 - 18 = 23
Since we're told the students received a score of 38, we know that answer choice C is incorrect.

It's also clear that, in order to achieve a score of 38, the student must get more than 41 questions right, which means we can also eliminate answer choices A and B.

MORE STRATEGY: At this point, I need only test ONE answer choice. For example, if I test answer choice D and it works, then I know the correct answer is D. Alternatively, if I test answer choice D and it doesn't work, then I know the correct answer is E.

Let's test choice D - 44
So, if the student correctly answered 44 questions, we know that the student incorrectly answered 6 questions.
Total score =44 - (2)(6) = 44 - 12 = 32
Since we're told the students received a score of 38, we know that answer choice D is incorrect.

By the process of elimination, the correct answer must be E.