Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 12 Oct 2011
Posts: 106
GMAT 1: 700 Q48 V37 GMAT 2: 720 Q48 V40

After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
14 Mar 2012, 04:03
Question Stats:
34% (02:36) correct 66% (02:15) wrong based on 524 sessions
HideShow timer Statistics
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.
source: gmathacks
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59264

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
14 Mar 2012, 05:33
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.
_________________




Retired Moderator
Joined: 16 Nov 2010
Posts: 1237
Location: United States (IN)
Concentration: Strategy, Technology

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
14 Mar 2012, 04:47
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
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 13 Sep 2015
Posts: 10

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
20 Oct 2015, 09:38
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 x40 32+ 50% (x40)  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  x40
Eq: 80% of total matches  ( 80% 0f first 40 + 50% of remaining) = 18 80% x  ( 32 + 50% (x40) = 18 .8x  32  .5x + 20 =18 .3x = 30 x = 100
Therefore total matches won  32 + 50% (10040) = 62 Sufficient
Answer : B



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8167
GPA: 3.82

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
22 Oct 2015, 13:30
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 spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 18 May 2016
Posts: 34

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
31 Jul 2017, 04:20
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+1/2n20. 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.



Intern
Joined: 22 Jan 2017
Posts: 30

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
23 Aug 2017, 22:25
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.



Intern
Joined: 30 Apr 2018
Posts: 2

After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
Updated on: 30 Apr 2018, 09:57
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.
Originally posted by duguena on 30 Apr 2018, 09:23.
Last edited by Vyshak on 30 Apr 2018, 09:57, edited 1 time in total.
Topic Merged. Refer to the above discussions.



Math Expert
Joined: 02 Sep 2009
Posts: 59264

Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
Show Tags
30 Apr 2018, 10:18
duguena wrote: 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.
_________________




Re: After winning 80% of his first 40 matches, Igby won 50
[#permalink]
30 Apr 2018, 10:18






