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30 Apr 2026, 19:00
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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.
The OA will be automatically revealed on Monday 4th of May 2026 07:00:06 PM Pacific Time Zone
(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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The OA will be automatically revealed on Monday 4th of May 2026 07:00:06 PM Pacific Time Zone
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.
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01 May 2026, 08:44
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Let:
Need total matches.
Statement (1)
x / (x + y + 4) = 1/4
4x = x + y + 4
3x = y + 4
y = 3x - 4 -----(1)
Not sufficient
Statement (2)
y / (x + y + 2) = 1/2
2y = x + y + 2
y = x + 2 ---------(2)
Not sufficient
Together
By solving equations (1) and (2), we can easily get the value of x and y, thus total games (x+y).
Ans (C)
- x = number of wins
- y = number of losses
Need total matches.
Statement (1)
x / (x + y + 4) = 1/4
4x = x + y + 4
3x = y + 4
y = 3x - 4 -----(1)
Not sufficient
Statement (2)
y / (x + y + 2) = 1/2
2y = x + y + 2
y = x + 2 ---------(2)
Not sufficient
Together
By solving equations (1) and (2), we can easily get the value of x and y, thus total games (x+y).
Ans (C)
Bunuel
