In order for a nursey to meet the condintions of its insurance there must be at least one adult present for every 4...

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Magoosh

In order for a nursery to meet the conditions of its insurance, there must be at least one adult present for every 4 children. The total number of children and adults at the nursery is 24. Is the nursery meeting the terms of its insurance?

1) The difference between the number of children and the number of adults is smaller than 15

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

OA D

[deloitte247]

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.