Parallelogram 43 • Level 5 • 26 Jun 2025Telescopes
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.
1.1 It is evening, and Meg, who is 1m tall, casts a shadow of length 3m. If Meg stands on her brother's shoulders, which are 1.5m above the ground, how long a shadow will she and her brother cast?
- 3m
- 4.5m
- 5.5m
- 6.5m
- 7.5m
- (Not answered)
The ratio of height to shadow length is 1:3. Their shadow will therefore be 3 × (1 + 1.5) m = 7.5m long.
2.
2.1 Seventy pupils (37 boys and 33 girls) are divided into two groups, with forty pupils in Group I and thirty pupils in Group II. How many more boys are there in Group I than there are girls in Group II?
- 4
- 7
- 8
- 9
- more information needed
- (Not answered)
Let the number of boys in Group I be
Let the number of boys in Group I be
Therefore there are 7 girls fewer in Group II than there are boys in Group I.
3.
3. 567 is multiplied by 3489. What is the units digit of the answer?
- 1
- 3
- 5
- 7
- 9
- (Not answered)
Take the units digits of any two numbers and multiply them together. The units digit of the answer is also the units digit of the product of the original numbers. As 7 × 9 = 63, the units digit of 567 × 3489 must also be 3.
4. Telescopes
Space scientist Maggie Aderin-Pocock talks about telescopes.
(If you have problems watching the video, right click to open it in a new window)4.1 Which type of telescope is less reliant on the quality of the glass?
- Refractive
- Reflective
- (Not answered)
5.
5.1 In how many whole numbers between 100 and 999 is the middle digit equal to the sum of the other two digits?
- 28
- 36
- 45
- 50
- 55
- (Not answered)
There are 9 such numbers whose first digit is 1 : 110, 121, 132, ..., 187, 198. Similarly there are 8 such numbers, beginning with 220 and ending with 297, whose first digit is 2; 7 such numbers, beginning with 330 and ending with 396, whose first digit is 3 and so on. Lastly there is only 1 such number whose first digit is 9: 990.
The answer, therefore, is 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45.
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... if not, then maybe next week.
- 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.
- The next Parallelogram is next week, at 3pm on Thursday.
- Finally, 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.