## Mathematics Technique 1 (trial and error)

### A practical lesson on how to optimise your trial and error skills for the Selective Test

## Mathematics Technique 1 (Trial and Error)

It is important to remember that the NSW Selective Test is multiple choice and it is often easier to use a trial and error (guess and check) approach to difficult and time consuming questions. When using trial and error in a question that has numeric answer options, do not go through each of the answer options from **A** to **D** but rather:

- Select an answer option that is not the smallest or largest
- Calculate whether this answer option is the correct option
- If the answer option attempted was not the correct option, select a new answer option to trial depending on whether the prior option resulted in a solution that was too large or too small

This will ensure that you will never have to try all the different answer options and will save you considerable time in the long run.

For example, if a student wanted to solve the following question sourced from our Selective Test online platform using trial and error:

Rachel has received marks of 14, 18, 16 and 17 out of 20 in the first four of five spelling exams.

What mark would she need in her last exam to get an average of 85%?

**A** 13

**B** 16

**C** 17

**D** 20

They would select an answer option that is not the smallest (13) or largest (20). In this case lets select 17. Then they would check if 17 is the correct option. The average of 14, 18, 16,17 and 17 is (14+18+16+17+17) / 5 = 16.4. It is clear that the correct answer option has to be larger than the trialled option of 17. Therefore they would check if the answer option bigger than 17 is the answer. The only option bigger than 17 is 20 and quickly redoing the calculation confirms that it is is the correct answer.

By using this method, the student has only needed to try 2 different options and will never have to try all 4 options in order to find the correct answer.