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.
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo