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81% (02:14) correct
19%
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A high school volleyball team completed its regular season last spring. If every match ended in either a win or a loss, with no ties, how many matches did the team play that season?
(1) If the team had lost 4 more matches than it actually lost, it would have won 25% of its matches.
(2) If the team had won 2 more matches than it actually won, it would have lost 50% of its matches.
(1) If the team had lost 4 more matches than it actually lost, it would have won 25% of its matches.
(2) If the team had won 2 more matches than it actually won, it would have lost 50% of its matches.
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02 May 2026, 03:30
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GMAT Club Official Solution:
A high school volleyball team completed its regular season last spring. If every match ended in either a win or a loss, with no ties, how many matches did the team play that season?
Let W be the number of wins and L the number of losses. Then total matches = W + L.
(1) If the team had lost 4 more matches than it actually lost, it would have won 25% of its matches.
If the team had lost 4 more matches, it would have won 4 fewer matches. So the number of wins would have been W - 4. The statement says that then the team would have won 25% of its matches, so:
W - 4 = 0.25(W + L)
3W - L = 16
This alone is not enough to find W + L.
Not sufficient.
(2) If the team had won 2 more matches than it actually won, it would have lost 50% of its matches.
If the team had won 2 more matches, it would have lost 2 fewer matches. So the number of losses would have been L - 2. The statement says that then the team would have lost 50% of its matches, so:
L - 2 = 0.5(W + L)
L - W = 4
This alone is not enough to find W + L.
Not sufficient.
(1)+(2) When combining we have two distinct linear equations with two unknowns, 3W - L = 16 and L - W = 4. We can solve for W and L and get the value of W + L. Sufficient.
Answer: C.
A high school volleyball team completed its regular season last spring. If every match ended in either a win or a loss, with no ties, how many matches did the team play that season?
Let W be the number of wins and L the number of losses. Then total matches = W + L.
(1) If the team had lost 4 more matches than it actually lost, it would have won 25% of its matches.
If the team had lost 4 more matches, it would have won 4 fewer matches. So the number of wins would have been W - 4. The statement says that then the team would have won 25% of its matches, so:
W - 4 = 0.25(W + L)
3W - L = 16
This alone is not enough to find W + L.
Not sufficient.
(2) If the team had won 2 more matches than it actually won, it would have lost 50% of its matches.
If the team had won 2 more matches, it would have lost 2 fewer matches. So the number of losses would have been L - 2. The statement says that then the team would have lost 50% of its matches, so:
L - 2 = 0.5(W + L)
L - W = 4
This alone is not enough to find W + L.
Not sufficient.
(1)+(2) When combining we have two distinct linear equations with two unknowns, 3W - L = 16 and L - W = 4. We can solve for W and L and get the value of W + L. Sufficient.
Answer: C.
General Discussion
01 May 2026, 02:19
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Let Wins = W, Losses = L, Total = W + L
Statement (1):
“If losses were 4 more → wins would be 25% of matches”
W / (W + L + 4) = 1/4
⇒ 4W = W + L + 4
⇒ 3W = L + 4
⇒ L = 3W − 4
We get one equation with two variables → infinitely many solutions. Not sufficient
Statement (2):
“If wins were 2 more → losses would be 50% of matches”
L / (W + L + 2) = 1/2
⇒ 2L = W + L + 2
⇒ L = W + 2
Again, one equation with two variables. Not sufficient
Stop here: still cannot determine W + L uniquely
Combine (1) and (2):
From (1): L = 3W − 4
From (2): L = W + 2
Now we have two equations, two variables. This is the point where we know it will be sufficient (you can stop here conceptually).
The answer is C.
Solve:
3W − 4 = W + 2
⇒ 2W = 6
⇒ W = 3
Then:
L = 5
Total = 8
GMAT Takeaway:
In DS, once you get independent equations = number of variables, you can stop and mark sufficient without solving completely.
Statement (1):
“If losses were 4 more → wins would be 25% of matches”
W / (W + L + 4) = 1/4
⇒ 4W = W + L + 4
⇒ 3W = L + 4
⇒ L = 3W − 4
We get one equation with two variables → infinitely many solutions. Not sufficient
Statement (2):
“If wins were 2 more → losses would be 50% of matches”
L / (W + L + 2) = 1/2
⇒ 2L = W + L + 2
⇒ L = W + 2
Again, one equation with two variables. Not sufficient
Stop here: still cannot determine W + L uniquely
Combine (1) and (2):
From (1): L = 3W − 4
From (2): L = W + 2
Now we have two equations, two variables. This is the point where we know it will be sufficient (you can stop here conceptually).
The answer is C.
Solve:
3W − 4 = W + 2
⇒ 2W = 6
⇒ W = 3
Then:
L = 5
Total = 8
GMAT Takeaway:
In DS, once you get independent equations = number of variables, you can stop and mark sufficient without solving completely.
