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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  [#permalink]

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New post 27 Jul 2014, 11:05
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E

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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.

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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 27 Jul 2014, 14:45
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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. The team won 0.6*65 = 39 of its first 65 games, we know nothing about the last 35 games. Not sufficient.

(2) The team won 60% of its last 65 games last season. The team won 0.6*65 = 39 of its last 65 games, we know nothing about the first 35 games. Not sufficient.

(1)+(2) Maximum number of games the team could have won is 39 + 39 = 78, for example if it won first and last 39 games. Minimum number of games the team could have won is 30 + 9 + 9 = 48, for example if it won first and last 9 games and 30 games which are the overlap of first 65 games and last 65 games. Not sufficient.

Answer: E.

Hope it's clear.
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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 27 Jul 2014, 12:37
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The trick here is that -

Between first 65 and last 65 -> 30 matched will overlap.
Since the team played only 100 matches,
=> 78-30 =48 < 50
Hence together also it will case will not be sufficient.
Option E !
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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 07 Jan 2018, 10:47
Bunuel 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. The team won 0.6*65 = 39 of its first 65 games, we know nothing about the last 35 games. Not sufficient.

(2) The team won 60% of its last 65 games last season. The team won 0.6*65 = 39 of its last 65 games, we know nothing about the first 35 games. Not sufficient.

(1)+(2) Maximum number of games the team could have won is 39 + 39 = 78, for example if it won first and last 39 games. Minimum number of games the team could have won is 30 + 9 + 9 = 48, for example if it won first and last 9 games and 30 games which are the overlap of first 65 games and last 65 games. Not sufficient.

Answer: E.

Hope it's clear.


Hi Bunuel,

I do not understand the combined portion.

How are we getting at 30+9+9 part?
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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 07 Jan 2018, 10:56
ashikaverma13 wrote:
Bunuel 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. The team won 0.6*65 = 39 of its first 65 games, we know nothing about the last 35 games. Not sufficient.

(2) The team won 60% of its last 65 games last season. The team won 0.6*65 = 39 of its last 65 games, we know nothing about the first 35 games. Not sufficient.

(1)+(2) Maximum number of games the team could have won is 39 + 39 = 78, for example if it won first and last 39 games. Minimum number of games the team could have won is 30 + 9 + 9 = 48, for example if it won first and last 9 games and 30 games which are the overlap of first 65 games and last 65 games. Not sufficient.

Answer: E.

Hope it's clear.


Hi Bunuel,

I do not understand the combined portion.

How are we getting at 30+9+9 part?


The overlap of the first 65 games and the last 65 games (out of 100) is middle 30 games: 100 = 65 + 65 - 30. The minimum number of games the team could have won is 30 (overlap) + 9 + 9 = 48.
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A sports team played 100 games last season. Did this team  [#permalink]

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New post 07 Jan 2018, 11:01
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ashikaverma13 wrote:
Bunuel 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. The team won 0.6*65 = 39 of its first 65 games, we know nothing about the last 35 games. Not sufficient.

(2) The team won 60% of its last 65 games last season. The team won 0.6*65 = 39 of its last 65 games, we know nothing about the first 35 games. Not sufficient.

(1)+(2) Maximum number of games the team could have won is 39 + 39 = 78, for example if it won first and last 39 games. Minimum number of games the team could have won is 30 + 9 + 9 = 48, for example if it won first and last 9 games and 30 games which are the overlap of first 65 games and last 65 games. Not sufficient.

Answer: E.

Hope it's clear.


Hi Bunuel,

I do not understand the combined portion.

How are we getting at 30+9+9 part?


Hi ashikaverma13

Here we need max & min values of games won. Max possible value is 39+39=78

Minimum value could be under a situation where there are 30 overlaps. So team won 78 matches by playing 65+65=130 games but in reality only 100 games were played. so 30 wins have been counted twice and hence need to be removed from the maximum value

i.e. 78-30=48 could be our minimum value.
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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 15 Jan 2018, 10:42
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WoundedTiger 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.


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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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 15 Jan 2018, 12:09
WoundedTiger 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.



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Assume a, b, c and d are numbers of games the team won from the first 35 games, the next 15 games, the next 15 games and the last 35 games, respectively.
The question asks if a + b + c + d ≥ 50.

Since we have 4 variables and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first, since we can save time by first checking whether conditions 1) and 2) are sufficient, when taken together.

Conditions 1) & 2)
a + b + c = 38 ( = 65 * 0.6)
b + c + d = 38 ( = 65 * 0.6)
a = 37, b + c = 1, d = 37 ⇒ a + b + c + d = 75 : Yes
a = 8, b + c = 30, d = 8 ⇒ a + b + c + d = 46 : No

Both conditions together are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: A sports team played 100 games last season. Did this team  [#permalink]

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New post 27 Jan 2019, 08:34
WoundedTiger 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.

\(\# \,{\rm{wins}}\,\,\,\mathop \ge \limits^? \,\,\,50\)

\(\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{first}}\,65\,\,{\rm{games}}\,\,\,\,\left( {1{\rm{st}}\,\,{\rm{till}}\,\,65{\rm{th}}} \right) \hfill \cr
\,39\,\,{\rm{wins}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{last}}\,65\,\,{\rm{games}}\,\,\left( {36{\rm{th}}\,{\rm{till}}\,\,100{\rm{th}}} \right) \hfill \cr} \right.\)

\({\rm{If}}\,\,{\rm{wins}}\,\,{\rm{games}}\,\,\# \,\,\left\{ \matrix{
\,1,2,3, \ldots ,39\,{\rm{and}}\,\,62,63, \ldots ,100\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\,\left( {78\,\,{\rm{games}}} \right) \hfill \cr
\,27,48, \ldots ,65\,\,{\rm{and}}\,\,36, \ldots ,74\,\,\, = \,\,\,27, \ldots ,74\,\,\,\,\,:\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\,\left( {48\,\,{\rm{games}}} \right) \hfill \cr} \right.\)


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

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A sports team played 100 games last season. Did this team  [#permalink]

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New post 01 May 2019, 15:22
Thanks for the great explanations and correct answer.
Just Bumping this interesting question and adding a tiny comment on it:
the minimum is 48 (at max. overlap of 30), but the maximum is 74 (at min. overlap of 4)
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A sports team played 100 games last season. Did this team   [#permalink] 01 May 2019, 15:22
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