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

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

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New post Updated on: 05 Oct 2019, 09:40
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Project IR Butler 2019-20 - Get one IR Question Everyday
Question # 05, Date : 05-Oct-2019
This post is a part of Project IR Butler 2019-20. Click here for Details


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

Originally posted by carbazzy on 07 Aug 2019, 13:07.
Last edited by SajjadAhmad on 05 Oct 2019, 09:40, edited 4 times in total.
Updated - Complete topic (16).
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Re: Of the 20 members in a local group of Mensa International, 40% are phi  [#permalink]

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New post 17 Sep 2019, 07:23
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


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
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Re: Of the 20 members in a local group of Mensa International, 40% are phi  [#permalink]

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New post 28 Jan 2020, 17:56
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 ????
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Re: Of the 20 members in a local group of Mensa International, 40% are phi   [#permalink] 28 Jan 2020, 17:56
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Of the 20 members in a local group of Mensa International, 40% are phi

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