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.

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
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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.
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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.

Please refer to the discussion above.
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