Parallelogram 45 • Level 5 • 10 Jul 2025The efficient detective

Noun: Parallelogram Pronunciation: /ˌparəˈlɛləɡram/

a portmanteau word combining parallel and telegram. A message sent each week by the Parallel Project to bright young mathematicians.

Tackle each Parallelogram in one go. Don’t get distracted.
Your score & answer sheet will appear immediately after you hit SUBMIT.
Don’t worry if you score less than 50%, because it means you will learn something new when you check the solutions.

1.

3 marks

1.1 30 ÷ 0.2 equals

1.5
6
15
150
600
(Not answered)

30 ÷ 0.2 = 300 ÷ 2 = 150, or 30 ÷ 0.2 = 30 ÷ 1/5 = 30 × 5 = 150.

2. Adjective order

This video by Tom Scott is nothing to do with maths, but it is interesting, so it’s worth two minutes of your time.

(If you have problems watching the video, right click to open it in a new window)

3.

5 marks

3.1 Inspector Remorse estimates that she can solve the average murder in x hours, a bank robbery in half that time, and a car theft in one third of the time she takes to solve a bank robbery. How many hours would she expect to take in solving two murders, six car thefts and four bank robberies?

3x
5x
6x
7x
12x
(Not answered)

Two murders: 2x hours;
Six car thefts: 6x6 = x hours;
Four bank robberies: 4x2 = 2x hours.

Total = 2x+x+2x hours = 5x hours.

4.

3 marks

4.1 Which is the largest of these fractions?

715
37
1123
49
611
(Not answered)

611 is the only one of these fractions which is greater than 12.

5.

4 marks

5.1 Timmy, Tammy and Tommy all have tummy ache! They all set off separately to visit their doctor, leaving their homes at exactly the same time. Timmy cycles the 8km to the surgery at an average speed of 20 km/h; Tammy walks the 1.2km to the surgery at an average speed of 4 km/h and Tommy drives the 16.5km to the surgery at an average speed of 45 km/h. In what order do they arrive at the surgery?

Tommy, Timmy, Tammy
Timmy, Tommy, Tammy
Tommy, Tammy, Timmy
Tammy, Timmy, Tommy
Tammy, Tommy, Timmy
(Not answered)

Timmy takes 24 minutes (8/20 of 1 hour) to reach the surgery; Tammy takes 18 minutes (12/40 of 1 hour) and Tommy takes 22 minutes (33/90 of 1 hour). The order, therefore, is Tammy, Tommy, Timmy.

Before you hit the SUBMIT button, here are some quick reminders:

You will receive your score immediately, and collect your reward points.
You might earn a new badge...
Make sure you go through the solution sheet – it is massively important.
A score of less than 50% is ok – it means you can learn lots from your mistakes.
If you missed any earlier Parallelograms, make sure you go back and complete them. You can still earn reward points and badges by completing missed Parallelograms.

Cheerio, Simon.