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# help me with an easier way !

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Manager
Joined: 09 Jun 2010
Posts: 67
help me with an easier way !  [#permalink]

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24 Jul 2010, 05:24
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Question Stats:

68% (02:00) correct 32% (03:12) wrong based on 46 sessions

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During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played ?

A 180
B 170
C 156
D 150
E 105

Thanks

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Re: help me with an easier way !  [#permalink]

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24 Jul 2010, 05:48
xmagedo wrote:
During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played ?

A 180
B 170
C 156
D 150
E 105

Thanks

Let $$x$$ be the games won after the first 100 games
& $$y$$ be the total number of games.

So, $$80 + x = 0.70 y$$

But $$x= \frac{(y-100)}{2}$$
So $$80 + \frac{(y-100)}{2} = 0.70$$
Solving for $$y$$ gives us the value $$150$$. So "D" is my pick.
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Re: help me with an easier way !  [#permalink]

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25 Jul 2010, 06:20
1
If you want to keep actual calculations to a minimum, think about this problem the following way: Overall, you want to have a success rate of 70%. The success rate of your first 100 games differs by 10 percentage points (80% - 70%) from the overall success rate, while the success rate of the other games differs by 20 percentage points (50% - 70%) from the overall success rate.

So to arrive at an average of 70%, the number of games with the higher success rate has to be twice that of the other games (20% / 10% = 2:1). Thus, the team played 100 +50*(1/2) = 150 games in total
Manager
Joined: 22 Jun 2010
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Re: help me with an easier way !  [#permalink]

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26 Jul 2010, 08:48
xmagedo wrote:
During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played ?

A 180
B 170
C 156
D 150
E 105

Thanks

Easiest way: Pick numbers!

What we know:
80% of 100 = 80 games
50% of x = 0.5x games

I started with D (my standard approach):
150 games - 100 games = 50 games
50% of 50 games = 25 games

80 won + 25 won = 105 won
70% of 150 = 105 won

Writing it down takes like 10x longer than the calculations in your head

Best,
André
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Re: help me with an easier way !  [#permalink]

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12 Aug 2010, 00:18
Draw a flowchart to understand the % question easily.please check attachment
Attachments

File comment: Check the flowchart
flowhcart.doc [36.5 KiB]

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Re: help me with an easier way !  [#permalink]

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19 Apr 2011, 19:28
let x be number of games played after initial 100 games.

so we got 80 + 0.5 x = 70 + 0.7 x

=> x =50

total games = 100+50 = 150

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Re: help me with an easier way !  [#permalink]

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19 Apr 2011, 20:50
(x+100)0.7 = 80 + 0.5x

=> 0.7x + 70 = 80 + 0.5x

=> 0.2x = 10

=> x = 50

Total = 100 + 50 = 150

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Re: help me with an easier way !  [#permalink]

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20 Apr 2011, 15:48
xmagedo wrote:
During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played ?

A 180
B 170
C 156
D 150
E 105

Thanks

This question can be orally solved using weighted averages (yet again!)
Of first 100 (w2) games, team won 80% (A2)
Of the remaining games, it won 50% (A1)
Overall the team won 70% (Aavg)

w1/w2 = (A2 – Aavg)/(Aavg – A1) = (80 - 70)/(70 - 50) = 1/2
Hence w1 = 50

Total number of games = 150
You can ofcourse use the scale method too.

If the formula and the term 'scale method' aren't making sense to you, check out:
http://www.veritasprep.com/blog/2011/03 ... -averages/
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Intern
Joined: 06 Apr 2011
Posts: 41
Re: help me with an easier way !  [#permalink]

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20 Apr 2011, 19:05
stanford2012 wrote:
If you want to keep actual calculations to a minimum, think about this problem the following way: Overall, you want to have a success rate of 70%. The success rate of your first 100 games differs by 10 percentage points (80% - 70%) from the overall success rate, while the success rate of the other games differs by 20 percentage points (50% - 70%) from the overall success rate.

So to arrive at an average of 70%, the number of games with the higher success rate has to be twice that of the other games (20% / 10% = 2:1). Thus, the team played 100 +50*(1/2) = 150 games in total

100 +50*(1/2) = 125 not 150! I think you meant 100 + 100* (1/2)?
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Joined: 06 Apr 2011
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Re: help me with an easier way !  [#permalink]

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20 Apr 2011, 19:12
VeritasPrepKarishma wrote:
xmagedo wrote:
During a certain season, a team won 80% of its first 100 games and 50% of its remaining games. If the team won 70% of its games for the entire season, what was the total number of games that the team played ?

A 180
B 170
C 156
D 150
E 105

Thanks

This question can be orally solved using weighted averages (yet again!)
Of first 100 (w2) games, team won 80% (A2)
Of the remaining games, it won 50% (A1)
Overall the team won 70% (Aavg)

w1/w2 = (A2 – Aavg)/(Aavg – A1) = (80 - 70)/(70 - 50) = 1/2
Hence w1 = 50

Total number of games = 150
You can ofcourse use the scale method too.

If the formula and the term 'scale method' aren't making sense to you, check out:
http://www.veritasprep.com/blog/2011/03 ... -averages/

Hi Karishma,
I was trying to solve this initially with the scale method. However, I'm finding it difficult to relate the ratios to the 'total number of games played'.

So this looks like:

50%----(20)----70%--(10)--80%

And the ratio would be 1:2. How come this translates to 150?
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Re: help me with an easier way !  [#permalink]

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18 Oct 2017, 09:31
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