Answer
False
Work Step by Step
If we take the numbers of admitted male and female applicants altogether:
Men in Department A: $2,000\times 0.5\times 0.6=600$
Men in Department B: $2,000\times 0.5\times 0.3=300$
Admitted male applicants: $900/2000=45\%$
Women in Department A: $100\times 0.6=60$
Women in Department B: $1,000\times 0.3=300$
Admitted male applicants: $360/1,100=33\%$
This is because female applicants tend to apply in Department B which is harder to get into.