Of all the attendees at a dinner party, 40% were women. If

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

D