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

[BTGmoderatorDC]

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

Source: Magoosh

[swerve]

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

Source: Magoosh

From the question, we know that \(C + A = 24\)

Considering statement (1) alone:
\(C - A < 15\)
\(\Longrightarrow\) Maximum \(C - A = 14\)
Solving for this, we get \(C = 19\) and \(A = 5\)
So, maximum value of \(C/A\) is \(3.8\)
Sufficient \(\Large{\color{green}\checkmark}\)

Considering statement (2) alone:
\(\dfrac{C - 1}{A + 1} = \dfrac{1}{3}\)
Solving the equation we get \(C/A = 3.8\)
Sufficient \(\Large{\color{green}\checkmark}\)

The correct answer is D