Foundation November 2023 Paper 1 Q25
25 Riley and Sam are conducting surveys.
They are both given the same list of 12 463 people from which to select their sample.
Riley selects every 56th person.
Sam selects every 64th person.
They both start counting from the first name in the list.
Work out how many people will be selected to be in both surveys.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 27 with correct working | 5 | M2 for [56 =] \(2 \times 2 \times 2 \times 7\) oe or better and [64 =] \(2 \times 2 \times 2 \times 2 \times 2 \times 2\) oe or better or listing the correct multiples of 56 and 64 up to 448 or M1 for [56 =] \(2 \times 2 \times 2 \times 7\) or better or [64 =] \(2 \times 2 \times 2 \times 2 \times 2 \times 2\) or listing the next 3 correct multiples of each or one complete list or [LCM =] \(448k\) (\(k = 2, 3, 4 \ldots\)) A1 for 448 or \(2^6 \times 7\) oe e.g \(8 \times 8 \times 7\) and M1 for 12 463 \(\div\) their 448 If 0, 1 or 2 scored, instead award SC3 for answer 27 with no working or insufficient working If 0 or 1 scored, instead award SC2 for answer 27.8… with no working or insufficient working If 0 scored, instead award SC1 for 448 with no working or insufficient working | “Correct working” requires evidence of at least either M2 or M1 M1 Allow factors in e.g. factor trees or tables and allow for M2 any correct complete method e.g. [56=] \(8 \times 7\) and [64=] \(8 \times 8\) or multiples of 56 up to 448 and some indication of dividing these numbers by 64 or with multiples of 64 and dividing by 56 multiples of 56 and 64 are 112, 168, 224, 280, 336, 392, 448 and 128, 192, 256, 320, 384, 448 You might see this:
Alternative method : M2 for an attempt at \(\frac{12463}{56} - \frac{12463}{64}\) or M1 for an attempt at \(\frac{12463}{56}\) and an attempt at \(\frac{12463}{64}\) AND B2 for 27.8…. or B1 for \(27 \lt\) their 27.8 \(\leqslant 28\) | ||||||||||||