Chocolate (Boys) = 8
Strawberry (Girls) = 9

(1) Total Children = 30.
We already know (8+9=17) what these 17 children had.

For max possible girls who had chocolate, consider all the remaining children to be girls.
Therefore, Chocolate(Girls) = 30-17=13. Sufficient.

(2) Fewer than half had strawberry. The total could be anything, above 19. We cannot say exactly how many girls would have had chocolate ice-cream.
AIMO

1) Exactly thirty children attended the party

Boys who had chocolate icecream = 8
Girls who had strawberry icecream = 9
Total number of students = 30

If the remaining students are girls and if we can find how many they are, we can answer the question posed. i.e [spoiler]and yes we can.Maximum possible # of girls = 30-9-8 = 13[/spoiler]

Sufficient

2) Fewer than half the children had strawberry ice cream

9 < (1/2)*Total number of students => 9 < (1/2)*(x+9+8) => x can be any number greater than 1

Insufficient - Option A