To get a job at Company X, an applicant must be recommended by three interviewers. Out of 30...

Question

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?

GMAT Panda · Accepted Answer

A We first name a variable for the number of applicants "recommended by all three interviewers". x = number of applicants recommended by all three interviewers We then calculate the total number of recommendations from the three interviewers. 15 + 17 + 20 = 52 We consider a scenario where each of the 30 applicants receives at most two recommendations. 2 30 = 60 Since 52 is less than 60, we can have no one recommended by all three interviewers, so the smallest possible value of x is 0. x = 0

Explanation	Calculations	Help
$We first name a variable for the number of applicants "recommended by all three interviewers" .$	$x = number of applicants recommended by all three interviewers$
$We then calculate the total number of recommendations from the three interviewers.$	$15 + 17 + 20 = 52$
$We consider a scenario where each of the 30 applicants receives at most two recommendations.$	$2 \times 30 = 60$
$Since 52 is less than 60, we can have no one recommended by all three interviewers, so the smallest possible value of x is 0.$	$x = 0$

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