Alan says, “If I add any four multiples of five, the total must be a multiple of 20.” Is he correct? You must show your working.
The key part of Alan statement is that he says the total must be a multiple of 20. This means that we only need to find one example to prove that he’s incorrect. The easiest way to approach the problem would be to consider the first four multiples of five. They are five, 10, 15, and 20 as they are the first four numbers in the five times table.
We need to work out the total. We do this by adding five, 10, 15, and 20. The total of the four numbers is 50. Alan said that this answer had to be a multiple of 20. Well, the multiples of 20 are the numbers in the 20 times table. They are 20, 40, 60, 80, and so on.
We can, therefore, say as 50 is not a multiple of 20, Alan is incorrect. There are lots of different multiples you could have chosen. We just need to find one example where Alan is incorrect.