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by yellowho » Thu Jan 27, 2011 1:31 am
After winning 80 percent of the Â…rst 40 matches he played, Igby
won 50 percent of his remaining matches. How many total
matches did he win?


(1) If Igby had won 50 percent of the total number of matches
he played, he would have lost 12 more total matches.
(2) If Igby had won 80 percent of the total number of matches
he played, he would have won 18 more total matches.

How are people translating the two statements into algebra? You can solve this without algebra but just wondering how people are setting up equations
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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Jan 27, 2011 2:00 am
yellowho wrote:After winning 80 percent of the 40 matches he played, Igby won 50 percent of his remaining matches. How many total matches did he win?

(1) If Igby had won 50 percent of the total number of matches he played, he would have lost 12 more total matches.
(2) If Igby had won 80 percent of the total number of matches he played, he would have won 18 more total matches.
Say, his remaining matches = 2x
Hence, total number of matches he played = (40 + 2x)
And, total number of matches he won = (80% of 40 + 50% of 2x) = (32 + x)
And, total number of matches he lost = (40 + 2x) - (32 + x) = (8 + x)

Statement 1: If he had won 50 percent of the total number of matches he played, then number of matches he would've lost = 50% of (40 + 2x) = (20 + x) = 12 + (8 + x) = 12 + Number of matches he actually lost.

Hence, no new information.

Not sufficient

Statement 1: If he had won 80 percent of the total number of matches he played, then number of matches he would've won = 80% of (40 + 2x) = (32 + 1.6x)

Hence, (32 + 1.6x) = (32 + x) + 18
We can easily determine the value of x from this equation.

Sufficient

The correct answer is B.
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by GMATGuruNY » Thu Jan 27, 2011 3:30 am
yellowho wrote:After winning 80 percent of the Â…rst 40 matches he played, Igby
won 50 percent of his remaining matches. How many total
matches did he win?


(1) If Igby had won 50 percent of the total number of matches
he played, he would have lost 12 more total matches.
(2) If Igby had won 80 percent of the total number of matches
he played, he would have won 18 more total matches.

How are people translating the two statements into algebra? You can solve this without algebra but just wondering how people are setting up equations
Statement 1:
Igby won 50% of the remaining matches.
He won 80% of the first 40.
To win 50% of all the matches, he must win 30% fewer of the first 40, resulting in 12 fewer wins:
.3*40 = 12.
Doesn't give us any information that we didn't already have.
Insufficient.

Statement 2:
Let R = remaining matches.
Igby won 80% of the first 40 matches.
He won 50% of R.
To win 80% of all the matches, he must win 30% more of R, resulting in 18 more wins:
.3R = 18.
R = 60.
Since he won .8*40 = 32 of the first 40 matches, total won = 32 + .5*60 = 62.
Sufficient.

The correct answer is B.
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