Andrew is thinking of a number
it is:
•between 1 and 150
•one more than a square number
•three less than a cube number
•it is not a prime number
what's his number?
you must show all your reasoning.

122

Step-by-step explanation:

Number is:

between 1 and 150 one more than a square number  = there are 12 square numbers, from 1²=1 to 12² = 144three less than a cube number , there are 5 cubes, 1³ = 1 to 5³ = 125it is not a prime number

Let's try the cubes because there are only 5 of them:

1³ = 1

it won't work as after subtracting 3 we get negative;

2³ = 8

subtract 3, we get 5 which is also 1 more than a square number of 4, however 5 is prime number so excluded;

3³ = 27

subtract 3, we get 24, it won't work as 23 is not a perfect square;

4³ = 64

subtract 3, we get 61, it won't work as 60 is not a perfect square, also 61 is a prime number;

5³ = 125

subtract 3, we get 122, which is 1 more than 11²= 121  and is not a prime number, so this is the required number;