Foundation June 2019 Paper 3 Q8
8 Four positive whole numbers add up to 84
One of the numbers is a multiple of 17
The other three numbers are equal.
What are the four numbers? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Subtracts 17, 34, 51 or 68 from 84 or subtracts any multiple of 3 from 84 or subtracts any three equal positive whole numbers from 84 | M1 | implied by 67, 50, 33 or 16 or implied by a multiple of 17 plus three positive whole numbers that sum to 84 or implied by a multiple of 3 and another positive whole number that sum to 84 or implied by four positive whole numbers, three of which are equal, that sum to 84 |
| Subtracts 17, 34, 51 or 68 from 84 and then divides by 3 or subtracts any multiple of 3 from 84 and then divides by 17 or subtracts any three equal positive whole numbers from 84 and then divides by 17 | M1dep | implied by 22.3(…), 16.6(…) or 16.7, 11 or 5.3(…) |
| 51, 11, 11, 11 | A1 | any order |
| Alternative method 2 | ||
| A correctly evaluated trial using addition of a multiple of 17 and three equal positive whole numbers or addition of a multiple of 17 and a multiple of 3 | M1 | |
| A different correctly evaluated trial using addition of a multiple of 17 and three equal positive whole numbers or addition of a multiple of 17 and a multiple of 3 | M1dep | |
| 51, 11, 11, 11 | A1 | any order |
Additional guidance
| Answer of 51 and 11 with indication of three 11s in working | M1M1A1 |
| Answer line blank with 51 and three 11s indicated as their four numbers | M1M1A1 |
| Answer line blank with 51 and three 11s in working | M1M1A0 |
| Answer of 51 and 11 with no indication of three 11s in working | M1M1A0 |
| 34, 20, 20, 10 implies first method mark as a multiple of 17 plus three positive whole numbers that sum to 84 | M1M0 |