Kai has four differently numbered cards - OCR - GCSE Maths - Question 2 - 2023 - Paper 1

For four numbers, the median is the average of the two middle numbers when organized in ascending order. Let the numbers be represented as $a_1, a_2, a_3, a_4$ where $a_1 < a_2 < a_3 < a_4$. The median is given by:

ext{Median} = rac{a_2 + a_3}{2} = 9

This implies that $a_2 + a_3 = 18$. As they are both prime numbers, we need to consider prime numbers close to 9.

The prime numbers between 5 and 19 are: 5, 7, 11, 13, 17, 19. We need to choose four prime numbers including 5 and 19, while also ensuring that their median is 9.

Considering combinations: (5, 7, 11, 19) gives a median of $\frac{7 + 11}{2} = 9$, which suits our condition.

We have already established that the lowest number is 5, and the combination of chosen numbers is (5, 7, 11, 19). Therefore, the numbers on the cards in order of size are: 5, 7, 11, 19.