A person inherited few gold coins from his father. If he put 9 coins in each bag then 7 coins are left over. However if he puts 7 coins in each bag then 3 coins are left over. What is the number of coins he inherited from his father.If he puts 9 coins in each bag then 7 coins are left over --> \(c=9q+7\), so # of coins can be: 7, 16, 25, 34, 43,
52, 61, ...
If he puts 7 coins in each bag then 3 coins are left over --> \(c=7p+3\), so # of coins can be: 3, 10, 17, 24, 31, 38, 45,
52, 59, ...
General formula for \(c\) based on above two statements will be: \(c=63k+52\) (the divisor should be the least common multiple of above two divisors 9 and 7, so 63 and the remainder should be the first common integer in above two patterns, hence 52). For more about this concept see:
http://gmatclub.com/forum/manhattan-rem ... ml#p721341,
http://gmatclub.com/forum/when-positive ... ml#p722552,
http://gmatclub.com/forum/when-the-posi ... l#p1028654\(c=63k+52\) means that # of coins can be: 52, 115, 178, 241, ...
(1) The number of coins lies between 50 to 120 --> # of coins can be 52 or 115. Not sufficient.
(2) If he put 13 coins in one bag then no coin is left over and number of coins being lesser than 200 --> # of coins is a multiple of 13 and less than 200: only 52 satisfies this condition. Sufficient.
Answer: B.
Would not the no of bag be same for both the scenarios "If he put 9 coins in each bag then 7 coins are left over. However if he puts 7 coins in each bag then 3 coins are left over" . If that be the case:
p and q above would be same constant. Please help in understanding this