An alternative method might be to restate the question by squaring both sides of the inequality. (raising 2 positive numbers to positive powers maintains the inequality).
"Is sqrt(n + k) > 2 sqrt(n)?" is equivalent to asking "Is n + k > 4 n? " or "is k > 3n?"
1) answers the question directly so A or D.
2) restated say k > 2n. if k > 2n we still don't know k's relationship to 3n so not sufficient, and not D, but A.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993