IMO (D)

Let's make a table

Lima| Brussel |
--------------------------------------
Like A | B |
Dislike C | D |

For the sake of convenience, Ive called these combos A,B,C,D.

Let there be x students in total

>2/3 dislikes lima beans (which also implies 1/3 like lima beans)
C = 2x/3 , A = x/3

>and of those who dislike beans, 3/5 also dislikes Brussels sprouts
D = 2x/5 , B = 3x/5

>How many students like Brussels sprouts but dislikes lima beans?
We need to find A + D = x/3 + 2x/5 = 11x/15

Both statement 1 and 2 give us the value of x, so each should be sufficient on its own.

Answer should Be D, ( even though the marked A First )

I missed the point that with II statement also we can get the answer.

thanks for posting such a brilliant question.