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Gambler

by Deepthi Subbu » Thu Nov 11, 2010 4:48 am
A professional gambler has won 40 % of 25 games that he played so far . Suddenly out of luck ,he wins 80 % of the time . Hence how many games should he play more to win 60 % of all the games??

1. 10
2.9
3.25
4.20
5.12
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by beat_gmat_09 » Thu Nov 11, 2010 5:09 am
Deepthi Subbu wrote:A professional gambler has won 40 % of 25 games that he played so far . Suddenly out of luck ,he wins 80 % of the time . Hence how many games should he play more to win 60 % of all the games??

1. 10
2.9
3.25
4.20
5.12
x - no of games played after 25 games.
40% of 25 = 10 = games won so far among 25 games played.
10+0.8x = total no. of games won, this should equal 60% of total games played. Total games played = 25 + x
10+0.8x = 0.6(25+x)
Solve for x, x = 25.
Cross check. Total games played = 25+x = 25+25=50. 60% of 50 = 30.
Games won after 25 games played = 0.8*25 = 20.
Total games won = 10 + 20 = 30 = 60% of 50.
Pick C.
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by fskilnik@GMATH » Thu Nov 11, 2010 5:52 am
Deepthi Subbu wrote:A professional gambler has won 40 % of 25 games that he played so far . Suddenly out of luck ,he wins 80 % of the time . Hence how many games should he play more to win 60 % of all the games??

1. 10
2.9
3.25
4.20
5.12
Sometimes choosing the variable we are looking for as "x" is not the easier as far as calculations are concerned... and another suggestion of mine is: try to avoid decimals, look the problem through "fractions-eyes"... I mean:

Exactly 10 games (from 25) already won, and we know that 4/5 of the remaining 5x ones (this will be what we are looking for!), that is, 4x games are expected to be victories, therefore from the fact that 60% is 3/5 we impose:

(10+4x) / (25+5x) = 3/5 therefore multiplying both sides by 5 we get

(10+4x)/(5+x) = 3 therefore 3(5+x) = 10 + 4x and hence 15 - 10 = x , to get 5x = 25 ... we are done!

Hope you like it.

Regards,
Fabio.
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by Deepthi Subbu » Thu Nov 11, 2010 5:56 am
Got where I went wrong.

Instead of calculating for 10 + .8 n = .6 ( n + 25) , I was calculating for 10 + .8 n = .6 (n +10) .
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by Deepthi Subbu » Thu Nov 11, 2010 5:59 am
Yet another method , thanks fskilnik. :)
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by fskilnik@GMATH » Thu Nov 11, 2010 6:14 am
Deepthi Subbu wrote:Yet another method , thanks fskilnik. :)
My pleasure, Deepthi Subbu! I usually say to my students that they have to "save energy/stamina, not only time", therefore the choices you make are the choices you will have to face with while solving the problems on the D-day... pay attention to that! ;)
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by MAAJ » Thu Nov 11, 2010 10:44 am
Deepthi Subbu wrote:A professional gambler has won 40 % of 25 games that he played so far . Suddenly out of luck ,he wins 80 % of the time . Hence how many games should he play more to win 60 % of all the games??

1. 10
2.9
3.25
4.20
5.12
Couldn't understand the problem :( if he ran out of luck isn't he supposed to have a lower win ratio? lower than 40? Is this a typo??? I'm confused...
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by Deepthi Subbu » Thu Nov 11, 2010 12:08 pm
Here suddenly out of luck means all of a sudden his luck changes and he gets to win more number of games .
Also initially he wins just 10 games ( 40 % out of 25 ) but he finally wants to win 60 % of all his games but a rate of 80 % . Hence this hints an increase.
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by MAAJ » Thu Nov 11, 2010 2:23 pm
Now I get it... so he wins 80% of all the next games. So the formula should be:

10 + 80%x = 60%
25 + x

if we solve for X it will be 25 :)

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