Practice Section (Princeton Review Math Workbook for GMAT)

Finished the last chapter–Practice Section (untimed).  Out of 37 problem solving and DS questions, I got 28 correct and 9 wrong.  Of the 9 mistakes, 2 were due to careless errors, and 1 error is one that I don’t agree.  Here’s the problem:

Three children, J, P, and R, are playing a game.  Each child will choose either the number 1 or the number 2.  When on child chooses a number different from those of the other two children, he is declared the winner.  If all of the children choose the same number, the process repeats until one child is declared the winner.  If R always chooses 2 and the other children select numbers randomly, what is the probability that R is declared the winner? 

I thought the answer was 1 out of 4 since these are the possible scenarios:

J, P, R = 1, 1, 2 or 1, 2, 2, or 2, 1, 2, or 2, 2, 2. 

But the answer in the book says 1/3.  I suppose if you don’t count the 2, 2, 2, as an actual outcome but as an intermediary round, then I can accept it.  If my logic is correct, then this is a lousy-worded question. 

Overall, I did a bit worse than I had expected.  I was expecting maybe 31 questions right and 6 questions wrong, but I guess it’s just more motivation to study harder.  One bright side is that of all the questions I got wrong, only 1 question was one where I was just stumped and I wouldn’t have gotten it right anyway.  Most of the mistakes were either due to carelessness or recalling certain things fast (just need to brush up on those topics).  Wish I could say the same about the GMAC Challenge problems…