Of the 20 members in a local group of Mensa International, 40% are phi

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

carbazzy

20 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
_________________

Thanks chetan2u

But the stimulus require us to “make only two selections”,so there must be “two” choices to be the correct answer???

shouldn’t we have to consider that,among those 12 people who are not philosopher,does it must be the condition that people have to choose between either they hold PhD or not hold PhD,or maybe there have other circumstance beside which people hold PhD and not hold PhD,since this will affect our collection


12 people who are not philosopher
There’re three conditions
PhD : not PhD
1 3
2 6
3 9
8 people who are philosopher
PhD : not PhD
7 1
add up
among these 20 people
PhD : not PhD
8 4
9 7 (no common factor to be divided up)
10 10

we can infer that there are two conditions
2:1&1:1 ????

The stimulus does not have the tabular format familiar to IR. It should look something like the following:

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 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
_______

chetan2

Thanks for the answer. But, how did you come up with the formula for PhD: 12* 1/(1+3)=3? Is that part of another formula from math?

And for Non-PhD, why did you do 12-3? Is the 12 from the non-philosophers?

Total phd=3+7
Total non phd= 9+1
x/y=10/10=1/1