Answer:
Step-by-step explanation:Yikes. Just so we’re all clear—this is not a real SAT question.
So far, Adam’s record is 6 wins/30 games. If he plays x more games, his record will be:
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You find the minimum x such that the fraction is greater than ½, which would mean he won more than ½ of his games.
Let’s do some math!
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So if he plays 54 more games, and wins 2/3 of them, he’ll have the same number of wins as losses. Check on that to make sure: He’ll have played 30 + 54 = 84 games, and won 6 + (2/3)54 = 42 of them. Yep, that works.
Now here is where it gets tricky (and why this question is not SAT-caliber). Remember that he’s losing 1/3 of his games. If his 52nd, 53rd, and 54th additional games were win, win, loss, then he would have had, very briefly, a winning record after his 53rd additional game.
His 55th additional game is another chance at a winning record. If he loses that game, then he’ll win the next two, and have a winning record for sure by the 57th additional game. From there, if he continues winning 2/3 of his games, he’ll have a winning record forever.
