Andrew is thinking of a number - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Question 3
Andrew is thinking of a number.
- It is between 1 and 150.
- It is one more than a square number.
- It is three less than a cube number.
- It is not a prime number.... show full transcript
Worked Solution & Example Answer:Andrew is thinking of a number - OCR - GCSE Maths - Question 3 - 2017 - Paper 1
Step 1
It is one more than a square number.
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
Let the square number be represented as n2. Then, Andrew's number can be expressed as x=n2+1.
Step 2
It is three less than a cube number.
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
Let the cube number be represented as m3. From the earlier expression, we have x=m3−3.
Step 3
Combine and solve.
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
Setting both equations equal gives us:
n2+1=m3−3
This simplifies to:
m3−n2=4
Step 4
Consider the range and prime condition.
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
We need values of m and n that satisfy this equation, with 1<x<150, and x should not be a prime number. Testing integers, we find:
For m=2, 8−12=4,
thus x=8−3=5 (a prime, discard).
For m=3, 27−52=4,
thus x=27−3=24 (not prime, valid).
Verifying: it is one more than 23 (a square) and three less than 27 (a cube).
Therefore, Andrew's number is 24.
