Dumsy_1711 wrote:
To get a job at Company X, an applicant must be recommended by three interviewers. Out of 30 applicants, 15 were recommended by the first interviewer 17 by the second interviewer, and 20 by the third interviewer. What is the least number of applicants who would have to have been recommended by all three interviewers
A 0
B 2
C 3
D 5
E 10
Can anyone tell me how to solve this please?
Think of this as a logical puzzle rather than a math problem.
Let's say the first interviewer recommended candidates numbered 1 to 15.
Now, when we try to think of which candidates were recommended by the second interviewer, we want to minimize the overlap. So, lets say they recommended candidates numbered 14 to 30.
There are now 2 candidates (numbered 14 and 15), who are recommended by 2 interviewers.
Now, when we try to think of which candidates were recommended by the third interviewer, we want to minimize the overlap with candidates recommended by both first and second interviewer. Basically, we want to try that the third interviewer does not recommend candidates numbered 14 and 15. Since the third interviewer recommends 20 candidates, this can easily be achieved if they recommend candidates numbered 1 to 10 and 21 to 30, for example.
Thus, the least number of applicants who would have to have been recommended by all three interviewers is 0.