Let the total no. of children = c
Let the total no. of adult = a
c+a=24
For every 4 children, there must be at least 1 adult ratio
c : a = 4 : 1
Target question: Is the nursery meeting the terms of its insurance?
Statement 1: The difference between the number of children and the number of adults is smaller than 15
c-a<15
The maximum possible value of c-a=14
c+a=24 --- eqn(1)
c-a=14 --- eqn(2)
a = 24 - c
c - 24 + c = 14
2c = 14 + 24
2c = 38
c = 38/2 = 19
If c=19, definitely, a=5.
Requirement=> 1a for 4c. So for 5a, it will be for 20c. Since c=19 and a=5, the requirement is met. Hence, statement 1 is SUFFICIENT.

Statement 2: If one more adult arrives at the nursery and one child is picked up by their parents, the ratio of adults to children will be 1:3
$$Therefore,\ \frac{C}{A}=\frac{C-1}{A+1}=\frac{3}{1}$$
Requirement: 4c to 1 adult since their present ratio is 3 children to 1 adult. They meet the requirement; hence, statement 2 is SUFFICIENT.

Since each statement alone is SUFFICIENT, option D is the correct answer.