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In a hiring procedure, applicants should be recommended by t

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by Max@Math Revolution » Thu Mar 03, 2016 5:29 pm
In a hiring procedure, applicants should be recommended by three interviewers. Of 30 applicants, 15 applicants were recommended by the first interviewer. 17 applicants were recommended by the second interviewer. 20 applicants were recommended by the third interviewer. What is the possible least number of the applicants recommended by all of the three interviewers?

A. 0
B. 2
C. 4
D. 5
E. 10


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by GMATinsight » Sat Mar 05, 2016 7:27 am
Max@Math Revolution wrote:In a hiring procedure, applicants should be recommended by three interviewers. Of 30 applicants, 15 applicants were recommended by the first interviewer. 17 applicants were recommended by the second interviewer. 20 applicants were recommended by the third interviewer. What is the possible least number of the applicants recommended by all of the three interviewers?

A. 0
B. 2
C. 4
D. 5
E. 10


* A solution will be posted in two days.
Please find the solution in the image attached

Answer: option A
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In a hiring procedure, applicants should be recommended by t

by Max@Math Revolution » Sun Mar 06, 2016 2:48 am
In a hiring procedure, applicants should be recommended by three interviewers. Of 30 applicants, 15 applicants were recommended by the first interviewer. 17 applicants were recommended by the second interviewer. 20 applicants were recommended by the third interviewer. What is the possible least number of the applicants recommended by all of the three interviewers?

A. 0
B. 2
C. 4
D. 5
E. 10

Image

->The above picture is possible. 20 applicant by the third interviewer avoid intersection and can be divided by each 10 for the first interviewer and the other 10 for the second interviewer respectively. Hence, 3 intersections is at least 0, which makes A the answer.
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In a hiring procedure, applicants should be recommended by t

by GMATGuruNY » Tue Mar 08, 2016 4:37 am
Max@Math Revolution wrote:In a hiring procedure, applicants should be recommended by three interviewers. Of 30 applicants, 15 applicants were recommended by the first interviewer. 17 applicants were recommended by the second interviewer. 20 applicants were recommended by the third interviewer. What is the possible least number of the applicants recommended by all of the three interviewers?

A. 0
B. 2
C. 4
D. 5
E. 10
Let:
F = the number recommended by the first interviewer.
S = the number recommended by the second interviewer.
T = the number recommended by the third interviewer.

Draw a VENN DIAGRAM:
Image

To MINIMIZE the value of FST, we must MAXIMIZE the values of FS, FT, and ST.

Since the total number of applicants = 30 and F=15, the greatest possible value for ST = 30-15 = 15:
Image

If ST=15, then the greatest possible value for FT = 20-15 = 5, and the greatest possible value for FS = 17-15 = 2:
Image

The diagram can be completed as follows:
Image

As illustrated by the resulting Venn Diagram, it's possible that FST = 0.

The correct answer is A.
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