Which statement correctly describes the ratio of the proportion of Group A that are over 65 to the proportion of Group B that are over 65 years of age at the end of the month?

Question

A study began the month with 30% of both Group A and Group B being over 65 years of age. During the 1^st month no new participants joined, but 10 people under 65 in group A and 5 people over 65 in Group B dropped out. Which statement correctly describes the ratio of the proportion of Group A that are over 65 to the proportion of Group B that are over 65 years of age at the end of the month?

a. it is 1:1

b. it is > 1

c. it is < 1

d. impossible to calculate without more information

Answer 1

For A, let there originally be A participants.

Then, .3A are over 65

Then, 5 removed are over 65 and 10 removed are under 65, for a total of A - 15, so the fraction over 65 are

(.3A - 5)/(A - 15) = (.3A - 4.5 - .5)/(A - 15) = (.3(A - 15) - .5)/(A-15) = .3 - 1/(2(A-15)) < .3

The ratio of Group A over 65 to the ratio of Group B over 65 is

< .3/.3 is < 1