1MA0 Foundation June 2012 Paper 2 Q20
20 Rani has 250 DVDs.
42% of her DVDs are thrillers.
\(\frac{2}{5}\) of her DVDs are comedies.
The rest of her DVDs are science fiction.
How many science fiction DVDs does Rani have? (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(250 - 0.42 \times 250 - 250 \div 5 \times 2\) \(= 250 - 105 - 100\) OR \(250 \times \left(1 - \left(\frac{42}{100} + \frac{2}{5}\right)\right) =\) \(250 \times \frac{9}{50}\) OR \(250 \times \left(\frac{100 - 42 - 40}{100}\right) =\) \(250 \times \frac{18}{100}\) OR \(250 - 250 \times \left(\frac{42}{100} + \frac{2}{5}\right) =\) \(250 - 250 \times \frac{41}{50} = 250 - 205\) OR \(250 - 250 \times \left(\frac{42}{100} + \frac{40}{100}\right) =\) \(250 - 250 \times \frac{82}{100} = 250 - 205\) | 45 | 4 | M1 for \(\frac{42}{100} \times 250\) oe (=105) M1 for \(\frac{2}{5} \times 250\) oe (=100) M1 for 250 − ‘105’ − ‘100’ A1 cao OR M1 for \(\frac{42}{100} + \frac{2}{5}\) \(\left(= \frac{82}{100}\right)\) or \(\left(= \frac{41}{50}\right)\) M1 for 1 − ‘\(\frac{82}{100}\)’ or 1 − ‘\(\frac{41}{50}\)’ M1 for ‘\(\frac{9}{50}\)’ \(\times 250\) A1 cao OR M1 for \(\frac{2}{5} \times 100\) or \(\frac{2}{5} = \frac{2 \times 20}{5 \times 20}\) or \(2 \times 20\) M1 for 100 − 42 − ‘40’ (= 18) M1 for ‘0.18’ \(\times 250\) A1 cao OR M1 for \(\frac{42}{100} + \frac{2}{5}\) \(\left(= \frac{82}{100}\right)\) or \(\left(= \frac{41}{50}\right)\) M1 for ‘\(\frac{41}{50}\)’ \(\times 250\) M1 for 250 − ‘205’ A1 cao OR M1 for \(\frac{2}{5} \times 100\) or \(\frac{2}{5} = \frac{2 \times 20}{5 \times 20}\) or \(2 \times 20\) M1 for ‘(42 + ‘40’)’/100 \(\times 250\) M1 for 250 − ‘205’ A1 cao |