Of 1000 applicants for a mountain-climbing trip in the Himalayas, 450 get altitu
ID: 3123866 • Letter: O
Question
Of 1000 applicants for a mountain-climbing trip in the Himalayas, 450 get altitude sickness, 622 are not in good enough shape, and 30 have allergies. An applicant qualifies if and only if this applicant does not get alltitude sickness, is in good shape, and does not have allergies. If there are 111 applicants who get altitude sickness and are not in good enough shape, 14 who get altitude sickness and have allergies, 18 who are not in good enough shape and have allergies, and 9 who get altitude sickness, are not in good enough shape, and have allergies, how many applicants qualify?
Explanation / Answer
Solution:
Let A is set who has altitude sickness :n (A) = 450
Let S is set who has not in good shape : n(S) = 622
and Let E is who has allergies : n(E) = 30
Now
other case are given
n(AS ) = 111
n(AE) = 14
n(SE) = 18
and
n(ASE) = 9
total number who doesn't qualify
n(ASE ) = n(A) + n(S) + n(E) -n(AS) -n(AE) -n(SE)-n(ASE)
= 450 +622+30 -111-25-18-9
= 939
total number applicant who qualify = 1000 - who doesn't qualify
= 1000 - 939
= 61
Answer: 61
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