Foundation November 2017 Paper 3 Q20
20 In a tennis tournament,
98 players took part in the singles only
34 players took part in the doubles only
twice as many players took part in the singles as took part in the doubles.
How many players took part in both the singles and the doubles?
You may use the Venn diagram to help you. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 of 3 | ||
| 98 in the singles non-intersecting part and 34 in the doubles non-intersecting part or \(98 + x\) or \(34 + x\) | M1 | |
| \(98 + x = 2(34 + x)\) | M1dep | oe \(\dfrac{1}{2}(98 + x) = 34 + x\) |
| \(98 + x = 68 + 2x\) | M1dep | oe \(49 + \dfrac{1}{2}x = 34 + x\) |
| 30 | A1 | |
| Alternative method 2 of 3 | ||
| 98 in the singles non-intersecting part and 34 in the doubles non-intersecting part | M1 | |
| \(34 \times 2\) or 68 or \(98 \div 2\) or 49 or 98 – 34 or 64 | M1 | second M1 implies M1M1 |
| 98 – their 68 or \(2 \times\) (their 49 – 34) or their 64 – 34 or \(2 \times\) their 64 – 98 | M1 | third M1 implies M1M1M1 |
| 30 | A1 | |
| Alternative method 3 of 3 | ||
| One complete trial correctly evaluated eg 98 + 10 = 108 and 34 + 10 = 44 and \(108 \div 2 = 54\) or \(44 \times 2 = 88\) (and No) | M1 | oe \(108 \div 2 = 54\) or \(44 \times 2 = 88\) is not required if a second trial is done |
| Second complete trial correctly evaluated eg 98 + 20 = 118 and 34 + 20 = 54 and \(118 \div 2 = 59\) or \(54 \times 2 = 108\) (and No) | M1 | oe \(118 \div 2 = 59\) or \(54 \times 2 = 108\) is not required if a third trial is done |
| Correct trial with both numbers and correctly evaluated 98 + 30 = 128 and 34 + 30 = 64 | M1 | |
| 30 | A1 | |
Additional guidance
| Working may be shown on Venn diagram | |
| 30 shown in intersection in Venn diagram unless contradicted by final answer | M1M1M1A1 |
| \(2 \times 98 - 2 \times 34 - 98\) oe | M1M1M1 |
| 98 and 34 correctly positioned in Venn diagram may be replaced by working or have additional working | |
| eg 34 in Venn diagram replaced by or with 68 | M1M1 |
| eg 98 in Venn diagram replaced by or with 49 | M1M1 |
| 98 and 34 incorrectly positioned in Venn diagram may be recovered by working |