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ExpertsGlobal5
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All the students in a group have opted for soccer, baseball, or both. 11 Feb 2026, 20:00
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All the students in a group have opted for soccer, baseball, or both. 90 percent of these students have opted for only one of the two. Overall, 180 students have opted for baseball. If 50 percent students have opted for baseball only, how many students have opted for only soccer?

A. 120
B. 150
C. 180
D. 270
E. 300


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All the students in a group have opted for soccer, baseball, or both. 12 Feb 2026, 06:46
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ExpertsGlobal5
All the students in a group have opted for soccer, baseball, or both. 90 percent of these students have opted for only one of the two. Overall, 180 students have opted for baseball. If 50 percent students have opted for baseball only, how many students have opted for only soccer?

A. 120
B. 150
C. 180
D. 270
E. 300


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Let’s consider a two set venn diagram



Set 1 denotes the baseball only,

Set 2 denoting soccer only.

While the common includes BOTH Soccer and Baseball.

All students choose either 1 or both. So, NEITHER =0.

if 90% opted for ONLY ONE of the two.

Then, 10% must have opted for both.

Moreover, 50% opted for Baseball ONLY.

Then 90% - 50% = 40% opted for Soccer ONLY.

Given 180 = Baseball = (50%+10%)

60% of total = 180

Total = 300.

Only Soccer = 40%*300 = 120.

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All the students in a group have opted for soccer, baseball, or both. 14 Feb 2026, 00:14
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BaseballNo baseballtotal
Soccer180-50x 100x-180 50x
No soccer50x0 50x
total180100x-180100x


we know 90% have opted for only one of those.
from our table we know the number of people for only one = 50x + 100x-180
and that is 90% of total
50x+100x-180 = 90x
X = 3
so using value of X, we can finish the whole table and find the students who only opted for soccer.

BaseballNo baseballtotal
Soccer30120 150
No soccer1500 150
total180120300

only for soccer = 120



ExpertsGlobal5
All the students in a group have opted for soccer, baseball, or both. 90 percent of these students have opted for only one of the two. Overall, 180 students have opted for baseball. If 50 percent students have opted for baseball only, how many students have opted for only soccer?

A. 120
B. 150
C. 180
D. 270
E. 300


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All the students in a group have opted for soccer, baseball, or both. 14 Feb 2026, 02:39
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This is a classic two-set overlapping groups problem, and the key concept being tested is translating percentage relationships into the standard Venn diagram formula.

Here's how I'd break it down:

1. Set up your categories. Every student falls into exactly one of three buckets: Soccer Only, Baseball Only, or Both. There's no "Neither" here since the problem says every student opted for at least one.

2. Use the 90% clue. 90% opted for only one of the two, which means Soccer Only + Baseball Only = 90% of total. That leaves Both = 10% of total.

3. Decode "180 students have opted for baseball." This means baseball TOTAL — including those who chose both. So: Baseball Only + Both = 180.

4. Use the 50% clue. 50% of all students opted for baseball only. So Baseball Only = 50% of total.

5. Find the total. Since Baseball Only + Both = 180, and Baseball Only = 50% and Both = 10%, we get 60% of total = 180. Total = 180/0.6 = 300 students.

6. Find Soccer Only. We know Soccer Only + Baseball Only = 90% of total. Baseball Only = 50%, so Soccer Only = 40%. That gives us 40% of 300 = 120.

Answer: (A) 120

Common trap: Many students read "180 have opted for baseball" and assume that's Baseball Only. It's not — it includes students who opted for both. The GMAT loves testing whether you distinguish between "total in a set" and "only in that set." Whenever a problem gives you both phrasings, pay close attention to which one includes the overlap.

Takeaway: On any overlapping sets problem, your first move should be defining whether each given number represents "only" or "total" for that category — getting this wrong is the #1 reason people miss these questions.
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All the students in a group have opted for soccer, baseball, or both. 14 Feb 2026, 08:30
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ExpertsGlobal5
All the students in a group have opted for soccer, baseball, or both. 90 percent of these students have opted for only one of the two. Overall, 180 students have opted for baseball. If 50 percent students have opted for baseball only, how many students have opted for only soccer?

A. 120
B. 150
C. 180
D. 270
E. 300
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