Past Paper Example 1
AQA Jun 2025 3H Q15
3 marks
Amy and Becky each make integers using **three** single digits.
In any integer, digits may be repeated.
• Amy makes **even** integers with a first digit greater than 7
• Becky makes **odd** integers with a first digit that is non-zero.
They each make as many different integers as possible.
In any integer, digits may be repeated.
• Amy makes **even** integers with a first digit greater than 7
• Becky makes **odd** integers with a first digit that is non-zero.
They each make as many different integers as possible.
How many **more** integers than Amy does Becky make?
Worked Solution & Mark Scheme (3 marks)
Amy: 1st digit ∈ {8, 9} (2 choices), 2nd digit (10 choices), 3rd digit even (5 choices) ⇒ 2 × 10 × 5 = 100 M1
Becky: 1st digit ∈ {1..9} (9 choices), 2nd digit (10 choices), 3rd digit odd (5 choices) ⇒ 9 × 10 × 5 = 450 M1
Difference = 450 – 100 = 350. A1
Becky: 1st digit ∈ {1..9} (9 choices), 2nd digit (10 choices), 3rd digit odd (5 choices) ⇒ 9 × 10 × 5 = 450 M1
Difference = 450 – 100 = 350. A1
Answer: Answer 350