QTS Numeracy Model Solutions – Test 2, Q20

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the Department for Education.

In this post, we look at question 20 from practice test 2. The full practice paper can be downloaded here​.

The Question

A school parents’ evening starts at 16:30 on each of two consecutive days.

A teacher has a total of 24 appointments lasting 10 minutes each and takes a 20 minute break each evening. The teacher filled all the available appointment slots on the first evening and finished at 19:00.

What is the earliest time the teacher can expect to finish on the second evening?

Give your answer using the 24-hour clock.

Worked Solution

This is a time question that is very typical of those that you will see on your numeracy skills test.

To answer questions like this, you will need to perform a few calculations and work step by step towards your solution. Each of the steps follows fairly simply from the previous step, so it is really about applying some logical thinking to the problem.

The question is asking you to work out what time the teacher will finish on the second parents evening. In order to do this, you will need to know the number of appointment slots that will be on the second evening. The question doesn’t tell you this directly, however, and instead tells you the total number of appointments so you would need to subtract the number of appointments on the first evening. You can work this out from the total amount of time the first evening takes, which can be calculated from the information given in the question.

To summarise, the steps that you will need to take to answer this question (in order) are:

1. Work out the total time in the first evening spent on appointments.
2. Work out the number of appointments on the first evening.
3. Work out how many appointments this leaves for the second evening.
4. Work out the time these appointments (plus the break) will take on the second evening.
5. Work out what time the second evening will finish.

Start by working out how much time was spent on appointments during the first of the parents evenings. The evening started at 16:30 and finished at 19:00, meaning that it lasted for two and a half hours in total. We need to work in minutes, so we can convert two and a half hours to 60 + 60 + 30 = 150 minutes.

The evening was made up of some appointments, plus a twenty minute break, so the amount of time spent on appointments would be 150 – 20 = 130 minutes.

Because each of the appointments lasts for 10 minutes, to work out the total number of appointments on that first evening, you just need to divide the total 130 minute time for appointments into 10 minute slots. 130 ÷ 10 = 13 appointments altogether.

Altogether there were 24 appointments across the two evenings, so if 13 are on the first evening, this must leave 24 – 13 = 11 for the second evening.

Work out how long this would take: 11 appointments at 10 minutes each will make a total of 11 × 10 = 110 minutes. There is also the 20 minute break to add on, which will make a total of 110 + 20 = 130 minutes. At this stage, it would be helpful to convert this time back into hours and minutes. To do this work out how many times 60 goes into 130. It goes in twice, with a remainder of 10, so the total time of the second evening is 2 hours and 10 minutes.

Add this on to the start time of 16:30 to get a finish time of 18:40.

The question asks for the answer to be given using the 24-hour clock, and it is already in this format, so 18:40 is the answer (note – because the other times in the question are expressed with the 24-hour clock, there is really no need to switch out of this format at any point).