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.