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

Question

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

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)

chetan2u · Accepted Answer

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

mimishyu · Answer

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 ????

Cellchat · Answer

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 |
_______

sssaniaa · Answer

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?

Kmohan1 · Answer

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

HarshZsssh · Answer

u dont require this formula to ans this question u need simple ratio understanding

11oadfalk · Answer

Can someone please confirm why the answer couldn't be 2:2 or 3:3 or 4:4, etc.? This is because we are told that x and y have no common factors greater than 1, correct?

GGGMAT2 · Answer

Why can't the answer be 2:2 or 3:3?

Bismuth83   would really appreciate if you could answer.

Nsp10 · Answer

for 2:2 {the common factor is 2 which is greater than 1 hence not allowed according to given condition {read the condition again}}

Sebastian55 · Answer

because 1:1 is the simplest form. Think about it. 10:10 could be 5:5 (5/5) but we could go even further and simplify that to 1:1.

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

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