GAIC Math 2024 Problem 124

Alice and Bob are playing a game. They write down four expressions on four cards: $x+y$, $x-y$, $x^2+xy+y^2$, and $x^2-xy+y^2$. They place these four cards face down on the table, then randomly choose one card to reveal its expression. Alice can pick two of the four cards and hand the other two to Bob, then all four cards are revealed. Alice can assign a value (real number) to one of the variables $x$ or $y$ and inform Bob of which variable she has assigned and what value. Afterwards, Bob assigns a value (real number) to the other variable. Finally, they each calculate the product of the values on their two cards, and the person with the larger product wins. Who has a winning strategy? A. Alice B. Bob C. Neither of them has a winning strategy.