A sports team played 100 games last season. Did this team win at least half of the games it played last season?
(1) The team won 60% of its first 65 games last season.
(2) The team won 60% of its last 65 games last season.
I found the explanation in MGMAT pretty long of checking the overlap. Can anyone help with a quicker way to solve this?
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reframing the question
did the team win >= 50 games
statement 1
first 65 games -> team won 65 * .6 = 39 games
last 35 games -> won between 0 and 35 games
hence,
39 + 0 < games won < 39 + 35
39 < games won < 74
INSUFFICIENT
statement 2
first 35 games -> won between 0 and 35 games
last 65 games -> team won 65 * .6 = 39 games
hence,
hence,
39 + 0 < games won < 39 + 35
39 < games won < 74
INSUFFICIENT
Statement 1 + 2
first 65 games -> team won 65 * .6 = 39 games
last 65 games -> team won 65 * .6 = 39 games
worst case - minimum wins - (maximum overlap of wins)
if we assume that team won all games from 36 - 65, it must have won 9 in first 35 and 9 in last 35 to satisfy given statements
i.e. 30 + 9 + 9 = 48
best case - maximum wins - (minimum overlap of wins)
if we assume that team won all of first 35 (0 - 35) and last 35 (66 - 100) games, it must have won 4 games in (36 - 65) range to satisfy given statements
i.e. 35 + 35 + 4 = 74
hence, 48 < games won < 74
INSUFFICIENT
did the team win >= 50 games
statement 1
first 65 games -> team won 65 * .6 = 39 games
last 35 games -> won between 0 and 35 games
hence,
39 + 0 < games won < 39 + 35
39 < games won < 74
INSUFFICIENT
statement 2
first 35 games -> won between 0 and 35 games
last 65 games -> team won 65 * .6 = 39 games
hence,
hence,
39 + 0 < games won < 39 + 35
39 < games won < 74
INSUFFICIENT
Statement 1 + 2
first 65 games -> team won 65 * .6 = 39 games
last 65 games -> team won 65 * .6 = 39 games
worst case - minimum wins - (maximum overlap of wins)
if we assume that team won all games from 36 - 65, it must have won 9 in first 35 and 9 in last 35 to satisfy given statements
i.e. 30 + 9 + 9 = 48
best case - maximum wins - (minimum overlap of wins)
if we assume that team won all of first 35 (0 - 35) and last 35 (66 - 100) games, it must have won 4 games in (36 - 65) range to satisfy given statements
i.e. 35 + 35 + 4 = 74
hence, 48 < games won < 74
INSUFFICIENT
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Target question: Did this team win at least half of the games it played last season?[email protected] wrote:A sports team played 100 games last season. Did this team win at least half of the games it played last season?
(1) The team won 60% of its first 65 games last season.
(2) The team won 60% of its last 65 games last season.
Rephrased target question: Did this team win more than 49 games?
Statement 1: The team won 60% of its first 65 games
In other words, the team won 39 of its first 65 games
Since we don't know the results of the last 35 games, we can't answer the target question with certainty. So, statement 1 is NOT SUFFICIENT
Statement 2: The team won 60% of its last 65 games
In other words, the team won 39 of its last 65 games
Since we don't know the results of the first 35 games, we can't answer the target question with certainty. So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Let's first see if the team could have won more than 49 games. To check this out, we'll MAXIMIZE the number of wins. So, let's say the team won the first 39 games (which would account for statement 1) and say the team won the last 39 games (which would account for statement 2)
So, in total, the team won 78 games. So, it is possible that the team won more than 49 games.
Now let's see if it's possible for the team to win fewer than 49 games. To do this, we'll MINIMIZE the number of wins by overlapping the shared wins for statements 1 and 2.
So, for statement 1, let's say the team lost games #1 to #26, and then won games #27 to #65 (39 wins)
For statement 2, let's say the team won games #36 to #74 (39 wins), and then lost games #75 to #100
So, in total, the team won games #27 to #74, which means it won 48 games altogether.
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
