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BongBideshini
Joined: 25 May 2021
Last visit: 16 Nov 2025
Posts: 46
Own Kudos:
Given Kudos: 58
Location: India
Concentration: Entrepreneurship, Leadership
Schools: HBS '26 Stanford '26 Wharton '26
GPA: 3.8
WE:Engineering (Aerospace and Defense)
11 Jul 2025, 10:01
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At a company with 36 employees, 23 are assigned to Project Alpha, and 18 are assigned to Project Beta. How many employees are assigned to both projects?
Expressing data in tabular form
Statement 1: Five employees are not assigned to either project
AB=10
So, Statement 1 is sufficient.
Statement 2: Exactly 21 employees are assigned to only one of the two projects.
That means we know that \({B}\bar{A}\) + \({A}\bar{B}\) = 21
Or, AB+ \(\bar{A}\bar{B}\) = 36-21 = 15,
But, we need AB . So, statement-2 is not sufficient
IMO, Ans A
Expressing data in tabular form
| A | \(\bar{A}\) | Total | |
| B | 18 | ||
| \(\bar{B}\) | 18 | ||
| 23 | 13 | 36 |
Statement 1: Five employees are not assigned to either project
| A | \(\bar{A} \) | Total | |
| B | 10 | 18 | |
| \(\bar{B}\) | 13 | 5 | 18 |
| 23 | 13 | 36 |
AB=10
So, Statement 1 is sufficient.
Statement 2: Exactly 21 employees are assigned to only one of the two projects.
That means we know that \({B}\bar{A}\) + \({A}\bar{B}\) = 21
Or, AB+ \(\bar{A}\bar{B}\) = 36-21 = 15,
But, we need AB . So, statement-2 is not sufficient
IMO, Ans A
11 Jul 2025, 10:04
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Statement 1 provides us with the number of employees who are not assigned to either project, using this information we can determine P(Total) = P(Project Alpha) + P(Project Beta) - P(Both) + P(Neither) --> 36 = 23 + 18 - x + 5 --> x = 10. Thus Statement 1 is sufficient. Statement two provides us with the not enough information to answer the question. Answer A.
Regards,
Lucas
Regards,
Lucas
Bunuel
11 Jul 2025, 10:06
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Total 36
Project Alpha = 23
Project Beta = 18
Question- How many present in both projects
Total = Alpha + Beta - Both + Neither
Statement 1:
(1) Five employees are not assigned to either project.
Neither =5
=> 36 = 23+18-Both+5 => Both = 10
Sufficient
Statement 2:
(2) Exactly 21 employees are assigned to only one of the two projects.
Alpha only + Beta only = 21
Alpha + Beta - 2*Both= Alpha only + Beta only
=> 41 - 2*Both = 21=>Both = 10
Sufficient
Hence answer is D
Project Alpha = 23
Project Beta = 18
Question- How many present in both projects
Total = Alpha + Beta - Both + Neither
Statement 1:
(1) Five employees are not assigned to either project.
Neither =5
=> 36 = 23+18-Both+5 => Both = 10
Sufficient
Statement 2:
(2) Exactly 21 employees are assigned to only one of the two projects.
Alpha only + Beta only = 21
Alpha + Beta - 2*Both= Alpha only + Beta only
=> 41 - 2*Both = 21=>Both = 10
Sufficient
Hence answer is D
Bunuel
