June 2024 Paper 2 Q9
9 A set of 4-digit integers each have
a first digit greater than 6
and
a second digit less than 8
What is the greatest possible number of integers in the set that are multiples of 5? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| 480 | B3 | B2 \(3 \times 8 \times 10 \times 2\) with at least three correct B1 \(3 \times 8 \times 10 \times 2\) with at least two correct or 3, 8, 10 and 2 identified with no others SC2 \(\dfrac{480}{10\,000}\) or \(\dfrac{1}{480}\) SC1 2400 or 720 or 189 |
Additional guidance
| eg1 \(3 \times 8 \times 10 \times 10\) product of exactly four numbers eg2 \(6 \times 7 \times 10 \times 2\) product of exactly four numbers eg3 \(3 \times 8 \times 10\) product of only three numbers eg4 \(24 \times 10 \times 10\) product of only three numbers eg5 840 no products | B2 B1 B0 B0 B0 |
| Products may be seen in any order eg1 \(2 \times 3 \times 8 \times 10\) eg2 \(10 \times 10 \times 2 \times 6\) | B2 B1 |
| Multiplication by 2 may be implied for B2 or B1 eg1 \(3 \times 10 \times 10 \times 1 + 3 \times 10 \times 10 \times 1\) eg2 \(3 \times 8 \times 10 \times 10 \div 5\) eg3 \(3 \times 7 \times 6 \times 1 + 3 \times 7 \times 6 \times 1\) eg4 \(3 \times 7 \times 10 \times 10 \div 5\) | B2 B2 B1 B1 |
| Examples of 3, 8, 10 and 2 identified with no others eg1 \(3 + 8 + 10 + 2\) eg2 \(\dfrac{3}{10} \times \dfrac{8}{10} \times \dfrac{10}{10} \times \dfrac{2}{10}\) (must be products) eg3 \(\dfrac{1}{3} \times \dfrac{1}{8} \times \dfrac{1}{10} \times \dfrac{1}{2}\) (must be products) | B1 B1 B1 |
| Ignore attempts to list the 4-digit integers | |
| 2400 is for ignoring the requirement for multiples of 5 | |
| 720 is for including 6 and 8 | |
| 189 is for excluding zero |