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.

findingmyself · Answer

How can one assume that Only Phd and Non Phd folks constitute philosophers. How is that possible without mentioning exclusively?

chetan2u · Answer

PhD and non PhD would include everyone...

A person may have any higher degree but we are not concerned with that.

Non Phd: It would include normal graduates, school dropouts and everyone else who do not have PhD degree.

egmat · Answer

Hi findingmyself,

This is a fair thing to question, and the good news is you don't need the word "exclusively" for it to hold. It's built into the way the two labels are phrased.

Look closely at the two groups the problem uses:

- those who  hold a PhD 
- those who  do not hold a PhD

The second group is simply the  negation  of the first. "Do not hold a PhD" isn't a separate, narrow category - it literally means "everyone who is not in the PhD group." So between the two labels, there is no one left over. Every member either has a PhD or doesn't; there is no possible third state.

That's different from the philosopher / non-philosopher split, which the problem  also  covers completely (" 40%  are philosophers and  the rest  are not"). Both splits are exhaustive - one by wording ("the rest"), the other by pure logic (hold vs. do not hold).

This is why chetan2u could take the  12  non-philosophers and split them cleanly into  3  PhD and  9  non-PhD, with nobody unaccounted for.

A quick way to feel it:  think of any yes/no property. "People who own a car" and "people who do  not  own a car" - together that's everyone, automatically. You'd never need the problem to add "and these are the only two groups," because the phrase "do not" already sweeps in the entire remainder.

So the ratio PhD : non-PhD covers all  20  members with no gap, giving  10  :  10  =  1 : 1 .

Answer: Column 1 (x) = 1; Column 2 (y) = 1

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

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

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