9. Alison, Bethany and Catherine are three sisters.
They are 6 years old, 7 years old and 12 years old.
Bethany is older than Alison.
Catherine’s age is a prime number.
What is each girls’ age?
Alison’s age ---------
Bethany’s age ---------
Catherine’s age ---------
23. Elizabeth writes down:
One multiple of 13; and
Two different factors of 77.
Elizabeth adds up her three numbers.
Her answer is greater than fifty but less than sixty.
What three numbers could Elizabeth have written down?
What is the link between whether a prime number can be expressed as the sum of two square numbers and the remainder when that prime number is divided by 4? If you are not sure you can extend the table above and see what happens for other prime numbers.