You really do not need any formula for this question. Also I can see no contraction between the statements.

After winning 80% of his first 40 matches, 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 --> Igby won 80% of his first 40 matches and 50% of the remaining matches, in order to win 50% of total matches he should have won 50% of his first 40 matches too (instead of 80%, so 30% less), which would have resulted in 0.3*40=12 more losses. So, this statement gives us the info we could deduce ourselves. Not sufficient.

(2) If Igby had won 80% of the total number of matches he played, he would have won 18 more total matches --> with the same logic he should have won 80% of the remaining matches, (instead of 50%, so 30% more). So 30% more winnings in the remaining matches (X) result in 18 more wins: 0.3*x=18 --> x=60 --> total matches won: 0.8*40+0.5*60=62. Sufficient.

Answer: B.
_________________

Let remaining matches be x

So Total matches won = 0.8 * 40 + 0.5 * x
The number of matches not won = 0.2 * 40 + Number of Matches Lost + Number of Matches drawn

1) 0.5 (40 + x) = 0.2 * 40 + Number of matches lost + 12

So x can’t be found, we don’t know the number of matches lost, because from the remaining %age (50% of x), there is no breakup for number of matches drawn.

2) 0.8(40 + x) = 0.8 * 40 + 0.5 * x + 18
So x can be found
Answer - B
_________________

After winning 80% of his first 40 matches, 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% of the total number of matches he played, he would have won 18 more total matches.

To me it seems that both statements contradict each other. The first one basically claims that he has only played 40 total games, while the second claims that he has played 62.5 matches.

Information given - won 80% of first 40 matches - 32, 50% of remaining matches
Information required - total matches won

If we can know the number of remaining matches we can know the desired answer

Statement 1 - If Igby won 50% of total matches he played, he would have lost 50% of the matches. It goes to follow that he would have won/lost 50% of his first 40 matches, which is equal to 20. The difference of 12 extra matches lost is accounted for in the first 40 matches and thus the information regarding 12 more matches lost is redundant. We still cannot find the answer to the question, Insufficient

eq : Let total matches be x, remaining matches x-40
32+ 50% (x-40) - 50% x = 12
32 + .5x - 20 - .5x = 12

Statement 2 : Lets form a simple algebraic equation to check whether statement 2 is sufficient.

Let total matches played - x
Remaining matches - x-40

Eq:
80% of total matches - ( 80% 0f first 40 + 50% of remaining) = 18
80% x - ( 32 + 50% (x-40) = 18
.8x - 32 - .5x + 20 =18
.3x = 30
x = 100

Therefore total matches won --- 32 + 50% (100-40) = 62 Sufficient

Answer : B

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

After winning 80% of his first 40 matches, 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% of the total number of matches he played, he would have won 18 more total matches.

To me it seems that both statements contradict each other. The first one basically claims that he has only played 40 total games, while the second claims that he has played 62.5 matches.

If we let the number of games remaining to be x, then this question only consists of 1 variable, but we are given 2 equations from the conditions, so there is high chance (D) is going to be our answer.
From condition 1, 0.5(40+x)=0.2*40+number of games lost+12. From this we cannot obtain the value of x, so this is insufficient (as there may be games drawn)
From condition 2, 0.8(40+x)=0.8*40+0.5x+18. From this we can achieve a unique solution for x, so this is sufficient. The answer is therefore (B).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

My answer:

What we really need to find is the number of matches n. Then we can apply the given percentages.
Statement 1 gives us, in equation: 1/2n=12+32+1/2n-20. n cancel out, no additional info. Insufficient.
Statement 2 gives us, in equation: 8/10n = 18 + 32 + 1/2n - 20. Can solve for n. Sufficient.

I really hate these problems. For me, it helps to look at the statements and think, "ok which side of the coin are we looking at wins or losses?" From there, you just try and construct the equation.

I try and think of it like a weighted average, which the GMAT really seems to like testing.

S1/

"Ok, we're on the losses side of the coin..."

0.5*(40 + x) = 8 + 0.5*(x) + 12 --> solve for x

20 + 0.5x = 20 + 0.5x
0 = 0 --> truism.

S2/

"Ok, we're on the wins side of the coin."

0.8*(40 + x) = 32 + 0.5*x + 18 --> solve for x

32 + 0.8x = 32 + 0.5x + 18
0.3x = 18
x = 18/0.3
x = 180/3
x = 60

Therefore he played 60 more matches, of which we won 30 and lost 30, so his overall number of wins was 32 + 30 = 62.

After winning 80 percent of the first 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.

Please refer to the discussion above.
_________________

[quote="BN1989"]After winning 80% of his first 40 matches, 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% of the total number of matches he played, he would have won 18 more total matches.

Lets say, Igby played 'n' matches in the second phase.

1) {.8*40 + .5 *n)} - .50(40+n) = 12, one equation and only one variable, we can get a unique value, but here n will get cancelled out, so insufficient.

2) 0.8 (40 +n ) - (32 + .5n ) = 18, or, 32 +.8n - 32 -.5n = 18, or, 0.3n = 18, n = 60. Sufficient.

B is the answer.