Kai has four differently numbered cards - OCR - GCSE Maths - Question 2 - 2023 - Paper 1
Question 2
Kai has four differently numbered cards.
- The range of the numbers is 14.
- The median of the numbers is 9.
- All the numbers are prime numbers.
- The lowest numbe... show full transcript
Worked Solution & Example Answer:Kai has four differently numbered cards - OCR - GCSE Maths - Question 2 - 2023 - Paper 1
Step 1
The range of the numbers is 14.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The range is defined as the difference between the highest and lowest numbers. Given the lowest number is 5 and the range is 14, we can calculate the highest number as follows:
extHighestNumber=extLowestNumber+extRange=5+14=19
Step 2
The median of the numbers is 9.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
With four numbers, the median is calculated as the average of the two middle numbers when arranged in order. Let the numbers be represented as a1,a2,a3,a4 where a1<a2<a3<a4. Given the median is 9, we can set up the equation:
rac{a_2 + a_3}{2} = 9
ightarrow a_2 + a_3 = 18
Step 3
All the numbers are prime numbers.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Prime numbers that can be considered include 5, 7, 11, 13, 17, and 19. Since the lowest number is 5 and the highest is 19, we need to find two other prime numbers that fit this criteria while also giving a median of 9.
Step 4
The lowest number is 5.
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the previous step, we can choose 7 and 11 as the next two prime numbers. Arranging them gives us 5, 7, 11, and 19. Checking the median:
rac{7 + 11}{2} = 9
This is correct. Thus, the numbers on the cards in order are: 5, 7, 11, 19.
