Of 1000 applicants for a mountain-climbing trip in the Himalayas, 450 get altitu

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 altitude 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

Number of aaplicants who will not qualify = 450+622+30 - (111+14+18) + 9 = 968

Number of aaplicants who will qualify = 1000 - 968 = 32

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