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A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A. 20
B. 25
C. 30
D. 35
E. 40
OA B
A professional gambler has won 40% of his 25 poker games for
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- Jay@ManhattanReview
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Say he plays x more games after he has played 25 games.AAPL wrote:Manhattan Prep
A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A. 20
B. 25
C. 30
D. 35
E. 40
OA B
Thus,
Number of games won out of the first 25 games = 40% of 25 = 10;
Number of games to be won out of the x games = 80% of x = 0.8x;
Number of games won out of the all (x + 25) games = 60% of (x + 25) = 3(x + 25)/5
Thus, 10 + 0.8x = 3(x + 25)/5;
50 + 4x = 3x + 75
x = 25 games
The correct answer: B
Hope this helps!
-Jay
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- fskilnik@GMATH
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The "aggressive-because-the-occasion-permits" style:AAPL wrote:Manhattan Prep
A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A. 20
B. 25
C. 30
D. 35
E. 40
60% is the average of 40% and 80% , therefore 25 games with 40% winning percentage and another 25 games with 80% winning percentage does the trick!
The solution is in red.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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- fskilnik@GMATH
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If you want the "let-me-be-prepared-for-the-general-case" style, you may follow Jay´s nice suggestion (above) or... use the alligation technique:AAPL wrote:Manhattan Prep
A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A. 20
B. 25
C. 30
D. 35
E. 40
$$? = x$$
$${{25} \over {25 + x}} = {{80 - 60} \over {80 - 40}} = {1 \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 25$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br
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- Scott@TargetTestPrep
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We are given that a poker player has won 0.4 x 25 = 10 poker games. If he starts winning 80% of his games, we need to determine how many more games must be played to have a winning percentage of 60% for the week. We can let x = the number of additional games played, and we set up the proportion:AAPL wrote:Manhattan Prep
A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?
A. 20
B. 25
C. 30
D. 35
E. 40
(10 + 0.8x)/(25 + x) = 60/100
(10 + 0.8x)/(25 + x) = 3/5
5(10 + 0.8x) = 3(25 + x)
50 + 4x = 75 + 3x
x = 25
Answer: B
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