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A sports team played 100 games last season. Did this team

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A sports team played 100 games last season. Did this team

by BTGmoderatorLU » Fri Jan 25, 2019 2:29 pm

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Source: Manhattan Prep

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.

The OA is E
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Jan 25, 2019 5:30 pm

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BTGmoderatorLU wrote:Source: Manhattan Prep

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.

The OA is E

Target question: Did this team win at least half of the games it played 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

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Brent
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by fskilnik@GMATH » Sun Jan 27, 2019 7:21 am

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BTGmoderatorLU wrote:Source: Manhattan Prep

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.
$$\# \,{\rm{wins}}\,\,\,\mathop \ge \limits^? \,\,\,50$$
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{first}}\,65\,\,{\rm{games}}\,\,\,\,\left( {1{\rm{st}}\,\,{\rm{till}}\,\,65{\rm{th}}} \right) \hfill \cr
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{last}}\,65\,\,{\rm{games}}\,\,\left( {36{\rm{th}}\,{\rm{till}}\,\,100{\rm{th}}} \right) \hfill \cr} \right.$$
$${\rm{If}}\,\,{\rm{wins}}\,\,{\rm{games}}\,\,\# \,\,\left\{ \matrix{
\,1,2,3, \ldots ,39\,{\rm{and}}\,\,62,63, \ldots ,100\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\left( {78\,\,{\rm{games}}} \right) \hfill \cr
\,27,28, \ldots ,65\,\,{\rm{and}}\,\,36, \ldots ,74\,\,\, = \,\,\,27, \ldots ,74\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\left( {48\,\,{\rm{games}}} \right) \hfill \cr} \right.$$


We follow the notations and rationale taught in the GMATH method.

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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