manik11 wrote:To make the school racquetball team, Larry must win at least 75% of his matches during tryouts. He must play a predetermined number of matches, none of which may end in a draw. If Larry wins every one of his remaining matches, he will finish with a winning percentage of exactly 75%. How many consecutive matches must Larry win?

1) Larry has already played 12 matches.
2) Larry has won 50% of the matches he has played.

OA : C
Source : Veritas Prep

Consider simple scenarios.
Statement 1 - Larry has played 12 matches. Scenario 1: Larry has won 7 of his 12 matches. In order to finish with a winning percentage of 75, he'll need to win his next 8 matches. (7 + x = .75(12+ x)

Scenario 2: Larry has won 6 of his 12 matches. In order to finish with a winning percentage of 75, he'll need to win his next 12 matches. (6 + x = .75(12+ x)

Because we get different results, this statement is not sufficient.

Statement 2 - Larry has won 50% of the matches he's played; we can reuse scenario 2 above. If he's won 6 of 12, he'll need to win 12 in a row.

Scenario 3: Larry has won 1 of 2 matches to start. He'll need to win 2 in a row to have won 75%.

Because we get different results, this statement is not sufficient.

Together we know that Larry has played 12 matches and won half of them. So he's won 6 games. That means we know he has to win the next 12 to get to a 75% winning percentage. Together the statements are sufficient. Answer is C