IMC 2013 Q15
15. I have a bag of coins. In it, one third of the coins are gold, one fifth of them are silver, two sevenths are bronze and the rest are copper. My bag can hold a maximum of 200 coins. How many coins are in my bag?
- A 101
- B 105
- C 153
- D 195
- E more information is needed
Intermediate Mathematical Challenge 2013, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 105
From the information given, we may deduce that the number of coins is a multiple of each of 3, 5, 7. Since these are distinct primes, their lowest common multiple is 3 × 5 × 7 = 105. So the number of coins in the bag is a multiple of 105. So there are 105 coins in the bag since 105 is the only positive multiple of 105 less than or equal to 200.
Solution © UK Mathematics Trust, from the IMC 2013 solutions. Longer versions with investigations: Solutions and investigations (PDF).