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# Key Stage 2

**Question 1. **The product of two numbers is 48 and the difference of these two numbers is 2

- What are the two numbers? Is it a unique solution? Why?

**Question 1.** The product of two numbers is 156 and the difference of these two numbers is 1

- What are the two numbers? Is it a unique solution? Why?

**Question 3.** The product of two numbers is 323 and the difference of these two numbers is 2

- What are the two numbers? Is it a unique solution? Why?

**Question 4**. I have 61 black socks when I put them in pairs how many pairs would I have? What do you notice?

- What about 73 red socks - how many pairs of red socks?
- What could you say if I had x socks - how many pairs?

**Question 5**. An octopus needs new socks for every day in June.

- How many pairs does she need? How many socks will she need?

**Question 6.** The 7 legged Conway monster that lives in the attic needs new socks for a year [not leap year]. She buys 1,246 pairs [that's a lot of socks!].

- Has she got enough? Has she got too many? Explain your answer.

**Question 7**. I have got x pairs of red socks and y pairs of yellow socks. How many ** socks** have I got altogether?

**Question 8**. Myself and some friends have all bought black socks for our secondary school uniform. Abdul bought w pairs; Petra bought fewer than Abdul, x pairs; Sally bought y pairs and I bought the difference between Abduls's amount of socks and Petra's amount of socks.

- In total we had M pairs of socks. Write an equation to show how many black socks we bought altogether.

**Question 9.** An apple and an orange costs 79p altogether. What could the cost of the apple and orange be? Work out 4 possible answers.

- The cost of the apple is an odd number. The cost of orange is an even number. Give two possible pairs of answers for the cost of the apple and orange.

**Question 10.** An apple and an orange costs 86p altogether.

Working systematically [ordered and organised] find:

- The cost of the apple is a prime number. The cost of orange is an odd number. Give three possible pairs of answers for the cost of the apple and orange.
- The cost of the apple is a square number. The cost of orange is an odd number. Give as many answers for the cost of the apple and orange that you can.
- The cost of the apple is a multiple of 7. The cost of orange is an odd number. Give as many answers for the cost of the apple and orange that you can.
- The cost of the apple is a factor of 64. The cost of orange is an even number. Give as many answers for the cost of the apple and orange that you can.
- The cost of the apple is a multiple of 8. The cost of orange is a multiple of 7. What is the cost of the apple and orange?

*Is the answer a unique solution? How do you know that? *

**Question 11. **An apple costs x pence and an orange costs y pence.

- Work out the total cost of 3 apples and 2 oranges.
- What is the difference in price between 4 apples and 6 oranges?