After winning 50 percent of the first 30 matches she played

Question

After winning 50 percent of the first 30 matches she played, Hortense won all of her remaining matches. How many total matches did she win?

(1) Hortense won 75 percent of the matches she played.
(2) If Hortense had won 50 percent of the total number of matches she played, she would have lost 15 more total matches.

Bunuel · Accepted Answer

After winning 50 percent of the first 30 matches she played, Hortense won all of her remaining matches. How many total matches did she win?

(1) Hortense won 75 percent of the matches she played.

Let the number of remaining matches be R, then we'd have 30 * 0.5 + R = (30 + R) * 0.75. With only one unknown, R, we can solve for it. Sufficient.

(2) If Hortense had won 50 percent of the total number of matches she played, she would have lost 15 more total matches -->

Hortense won  50% of her first 30 matches  and  100% of the remaining matches . To win 50% of the total matches, she should have won only  50% of the remaining matches  (instead of 100%, so 50% less). So, 50% losses in the remaining matches (R) result in 15 more losses: 0.5 * R = 15 → R = 30 → total matches won: 30 * 0.5 + 30 * 1 = 45. Sufficient.

Answer: D.

AbeinOhio · Answer

I set this up so that additional matches won are X

Based on info provided initially
person won 15 lost 15 and additionally won X

1) so (15 + x)/(15 + 15 + x) = 75/100

Sufficient

2) similar situation

50/100 = (15+x-15)/(15 + 15 + x)

Sufficient

boomtangboy · Answer

Hi ,

I solved it a little differently so might help

First 30 Games Remaining Games Total Games
Won 15 Games x Games 15 + x Games
Lost 15 Games 0 Games 15 Games
Total : 30 Games x Games 30 + x Games

Statement 1 : 15+x = .75 ( x+ 30 )
Hence sufficient

Statement 2 : 0.50 ( x+30 ) = 15 + 15

hence sufficient

I hope this helps :-)

Raghunathnallu · Answer

After winning 50 percent of the first 30 matches she played, Hortense won all of her remaining matches. How many total matches did she win?

(1) Hortense won 75 percent of the matches she played. Say # of remaining matches is R: 30*0.5+R*1=(30+R)*0.75, we have only one unknown R, hence we can solve for it. Sufficient.

(2) If Hortense had won 50 percent of the total number of matches she played, she would have lost 15 more total matches --> Hortense won 50% of his first 30 matches and 100% of the remaining matches, in order to win 50% of total matches she should have won 50% of the remaining matches (instead of 100%, so 50% less). So 50% losses in the remaining matches (R) result in 15 more losses: 0.5*R=15 --> R=30 --> total matches won: 30*0.5+30*1=45. Sufficient.

Hi There - Is there any way you can explain the second point again please

Bunuel · Answer

Please elaborate what exactly was confusing there. Thank you. Meanwhile check similar questions to practice: after-winning-80-percent-of-the-fi-rst-40-games-it-played-129338.html a-chess-player-won-25-percent-of-the-first-20-games-152608.html after-winning-80-of-his-first-40-matches-igby-won-129062.html after-winning-50-percent-of-the-first-x-games-it-played-149675.html after-winning-30-percent-of-the-first-50-games-it-played-142267.html after-winning-50-percent-of-the-first-20-games-it-played-te-167045.html Hope this helps.

ayushee01 · Answer

1) she won 75% of total matches means she did not win 25% of matches , which is 50% of first 30 matches(=> 15 matches), since she won all the remaining matches . 
let total matches be x , 25% of x=15
x=60 , hence sufficient

2) if for 50% win she lost 15 more matches, total match not won = 30 , total matches = 2(30) = 60
hence, sufficient

arunavamunshi1988 · Answer

When it is said that out of 30 matches 50% of matches are won, i.e 15 matches are won. How can I assume that 15 matches were lost? There could be a tie unless specifically mentioned that no tie is possible. So in that case I assume ans would be A. What do u say guys?

T1101 · Answer

One could also think of it in terms of ratios:

S(1)   \frac{75}{100}=\frac{Total Games Won}{Total Games Played}=\frac{15+x}{30+x} 
 --> x=30 , so  Total Games Won :  15+30=45

S(2)   \frac{50}{100}=\frac{Total Games Won}{Total Games Played}=\frac{15+x}{30+2x} 
 --> x=30 , so  Total Games Won :  15+30=45

pierjoejoe · Answer

0.5*30 + (total-30) = won
15 + total -30 = won
total -15 = won

we need the total to find the number of winnings

(1) gives won/total = 75% --> we can find total and therefore solve the equation

(2) this one is tricky but it can be translated in:
SUFFICIENT 
if she won 15 less matches, she would have won 50% of the games:

(won-15)/total = 50%

we can therefore find total and the number of winnings.

SUFFICIENT

After winning 50 percent of the first 30 matches she played

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