In a poker game, Janice's and Ralph's combined earnings totaled $150.

Dear AbdurRakib,
I'm happy to explain.

We are told these two individuals are playing poker. Often poker is played by a group, but it is possible for just two people to play poker. If both Janice and Ralph won money in the game, then we know for a fact that they weren't playing just each other. There must have been at least one more person, some person or people who took the $150 loss on the other side of the $150 gain of these two.

Statement #1: Ralph's winnings equaled \(\frac{1}{2}\) of Janice's winnings
So, Ralph's winnings are "one part" and Janice's are "two parts," so together, the $150 represents "three parts." Ralph won $50 and Janice won $100. This statement leads directly to a definitive numerical answer to the prompt question. This statement, alone and by itself, is sufficient.

Statement #2: Ralph won 10% of all the money won in the game.
"All the money in the game" would mean the total amount bet by all players playing. How many players are playing? We don't know. Were Ralph and Janice the only players who gained money? Did other people gain money also? There's a ton we don't know, so we have no way to compute the total amount of money in the game. This statement, alone and by itself, is not sufficient.

First statement is sufficient, second isn't. OA = (A)

Just to make sure you are familiar with the terminology: suppose Janice, Ralph, Chris, Kevin, and I play poker. Suppose we each come to the table with $100, and at some point, each one of us has all that money in at least one bet on the table. This means there is $500 in the game. Now suppose at the end of the game:
Janice walks away with $200
Ralph walks away with $150
Chris walks away with $100
Kevin walks away with $50
I walk away with $0
Then we would say, Janice has won $100 or netted $100 or cleared $50. Ralph netted $50.
Chris broke even: he left the game with the exact same amount with which he started.
Kevin has lost $50, or he is out $50, and I am out $100.
That's the basic terminology concerning financial gains & losses in poker.

Does all this make sense?
Mike