Overlapping Sets

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Overlapping Sets

by swerve » Tue May 19, 2020 6:42 am

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Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?

A. 0
B. 2
C. 6
D. 8
E. 12

The OA is A

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Tue May 19, 2020 6:42 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: Overlapping Sets

by deloitte247 » Sat May 23, 2020 1:36 am

Given that an applicant can only be admitted when all interviewers gave admission

Target question => At least how many applicants get the admission?

Interviewer A admitted 15 applicants
Interviewer B admitted 17 applicants
Interviewer C admitted 20 applicants
Total applicants = 40

Assuming that all the 15 applicants admitted by A are also part of the 17 admitted by B then 17 applicants are admitted by at least one of either interviewer A or B
Applicants admitted by A and/or B = 17
17 + 20 = 37

Since 37<40 (total applicants) it is possible that none of the 17 applicants admitted by A or B are also admitted by C. Hence, there is a possibility that none of the applicants were admitted by all the three interviewers

Therefore, the least number of admitted applicants = 0
Answer = A

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Overlapping Sets

by Scott@TargetTestPrep » Sun May 31, 2020 4:08 am

swerve wrote: ↑
Tue May 19, 2020 6:42 am
Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer A admitted 15 applicants, B admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?

A. 0
B. 2
C. 6
D. 8
E. 12

The OA is A

Solution:

We can assume all 15 applicants admitted by A are also 15 of the 17 applicants admitted by B. Thus, so far, 17 applicants are admitted by at least one of the two interviewers A and B. However, since 17 + 20 = 37 < 40, it’s possible that none of these 17 applicants who are admitted by A and/or B are admitted by C, so the least number of applicants admitted by all three interviewers is 0.

Answer: A

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