Juliet has attempted 213 problems and solved 210 of them correctly. Her friend Romeo has just started, and has attempted 4 problems and solved 2 correctly. From now on, Juliet and Romeo will attempt all the same new problems. Find the minimum number of problems they must attempt such that it is possible that Romeo's ratio of correct solutions to attempted problems will be strictly greater than Juliet's.

Question

mathmale · Answer

First of all, does it seem possible that our friend Romeo could ever surpass the success rate of his sweetie Juliet?  Juliet's success rate is 210 successes in 213, or 210/213, whereas poor Romeo's is only 2/4, or 1/2.   Personally, I don't see how Romeo is ever going to do better than Juliet.  and you?

anonymous · Answer

I also don't have any hope if he would ever make it but I need to know how to solve this.

mathmale · Answer

I've borrowed this phrase from the problem statement:  "Find the minimum number of problems they must attempt such that it is possible that Romeo's ratio of correct solutions to attempted problems will be strictly greater than Juliet's."

Romeo's ratio of correct solutions to attempted problems is simply 2/4, or 1/2.  Juliet's is 210/213.  If there is any way in which 1/2 could ever be "strictly greater than" 210/213, I surely don't know it.  What conclusion could you draw from that?

anonymous · Answer

Wait! I am trying something.