All the students in a group have opted for soccer, baseball, or both.

Question

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

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

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler

Dereno · Answer

Let’s consider a two set venn diagram https://gmatclub.com/forum/download/file.php?id=87784 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. Option A GMAT-Club-Forum-zcga5cv1.png

vasu1104 · Answer

Baseball 
 No baseball 
 total 
 
  Soccer 
 180-50x  
 100x-180 
  50x 
 
  No soccer 
 50x 
 0 
  50x 
 
  total 
 180 
 100x-180 
 100x

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.

Baseball 
 No baseball 
 total 
 
  Soccer 
 30 
 120 
  150 
 
  No soccer 
 150 
 0 
  150 
 
  total 
 180 
 120 
 300

only for soccer = 120

Edskore · Answer

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.

ExpertsGlobal5 · Answer

Video explanation:    https://www.youtube.com/watch/3uB8w8aB-tE  https://www.youtube.com/watch?v=3uB8w8aB-tE

All the students in a group have opted for soccer, baseball, or both.

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	Baseball	No baseball	total
Soccer	180-50x	100x-180	50x
No soccer	50x	0	50x
total	180	100x-180	100x

GMAT Problem Solving (PS) Questions

All the students in a group have opted for soccer, baseball, or both.

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