carbazzy wrote:
Of the 20 members in a local group of Mensa International, 40% are philosophers and the rest are not. Among those who are not philosophers, the ratio of those who hold a PhD to those who do not hold a PhD is 1:3. Among those who are philosophers, the ratio of those who hold a PhD to those who do not hold a PhD is 7:1. For all 20 members, the ratio of those who hold a PhD to those who do not is x : y , where x and y have no common factor that is greater than 1.
Select for x and for y values that are jointly consistent with the information provided.
Make only two selections, one in each column.
(The numbers are the same for X and Y)
x y
1
2
3
4
5
carbazzy20 members..40% are philosophers = 0.4*20=8,
Ratio of PhD to Non Phd = 7:1... so Phd = 7 and Non PhD = 1
Remaining are non philosophers = 20-8=12,
Ratio of PhD to Non Phd = 1:3... so Phd = \(12*\frac{1}{(1+3)}=3\) and Non PhD = 12-3=9
Ratio PhD:NonPhD=(7+3):(1+9)=10:10=1:1
Hope it helps