Of all the attendees at a dinner party, 40% were women. If each attendee arrived at the party either alone or with another attendee of the opposite sex, what percentage of the total number of attendees arrived at the party alone?
(1) 50% of the male attendees arrived with a woman.
(2) 25% of the attendees arriving alone were women.
60% of the attendees were men, so if the number of attendees was n, the number of men was 0.6n.
(1) Half of the 0.6n male attendees arrived with a women, so the number of women was 0.3n+ the number of women who arrived alone. Thus the number of women who arrived alone was n-0.3n-0.6n=0.1n, and the number of people who arrived alone was 0.1n (women)+0.3n (men), i.e 40% of the total.
(1) is sufficient
(2) If k is the number of women who arrived alone, 3k men arrived alone. The rest of the people arrived with a member of the opposite sex, so the number of men-the number of women=2k=0.2n, where n is the number of attendees. Thus 4k (the number of people who arrived alone) is 0.4n, 40% of the total
(2) is sufficient