Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Number 3
19 practice questions
Practice questions
1–4 of 4 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A school is holding a sports day with relay races. There are 198 boys and 135 girls. Each relay team must have the same number of boys and the same number of girls, and no students can be left out.
Find the greatest number of teams that can be formed and state how many boys and how many girls would be in each team.
Question 2
5 marks · Hard
Answer and see the solution →Let N = 2940.
(a)[2 marks]Express 2940 as a product of its prime factors in index form.
(b)[2 marks]Given that M = 2940 × 42, write M as a product of its prime factors in index form.
(c)[1 mark]Hence or otherwise, find the highest common factor (HCF) of 2940 and 42.
Question 3
4 marks · Hard
Answer and see the solution →Three bells ring together at 09:00. The first bell rings every 36 minutes, the second every 54 minutes, and the third every 81 minutes.
What is the next time all three bells will ring together? Show your working clearly.
(a)[3 marks]Find the lowest common multiple (LCM) of 36, 54, and 81.
(b)[1 mark]State the next time (in hours and minutes) after 09:00 that all three bells will ring together.
Question 4
4 marks · Hard
Answer and see the solution →A number n is such that it has exactly 4 positive factors, and n is less than 100.
List all possible values of n and explain your reasoning.
(a)[2 marks]List all the numbers less than 100 with exactly 4 positive factors.
(b)[2 marks]Explain how you determined these numbers.