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# Set Theory

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Intern
Joined: 15 Mar 2013
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12 Apr 2013, 15:33
I have a hunch that this is not the right place to ask this question

Nevertheless,

Question is:

In set theory( overlapping sets), if the question speaks about 3 sets ( A,B and C) and mentions that x is present in set A as well as set B. Does that mean A is in A∩B and not in A∩B∩C?

Or does that mean x is atleast in A∩B.

I personally would go with the latter but I am having a hard time convincing the local tutors. Please help.

Let me also post the question I am referring to, and the answer provided by a local coaching institute.

The teachers' colony has 2800 members, out of which 650 members read only english newspaper.550 members read only Hindi newspaper and 450 members read only marathi newspaper. Number of members reading all the newspapers is 100.Members reading Hindi as well as English newspaper are 200,Hindi as well as Marathi, 400 and members reading english and marathi is 300.

1-Difference between English as well as Marathi and English as well as Hindi.

2-Number of members reading atleast 2 newspapers.

Answers (Which I presume are not correct)

1-100
2-1000
3-1250
4-1650
5-150

Last edited by Zarrolou on 13 Apr 2013, 09:40, edited 1 time in total.
Renamed (from "Ttheory")
MBA Section Director
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13 Apr 2013, 09:35
Hi,
In my opinion, either the question typed incorrectly, or it is incorrect.
The language of question is confusing. Here i attempted to solve it as follows.
Total Members = 2800
E ONLY= 650
H ONLY= 550
M ONLY = 450
ALL = 100
H + E = 200 ----------> H + E ONLY = (H + E) - ALL = 200 - 100 = 100
H + M = 400 ----------> H + M ONLY = (H + M) - ALL = 400 - 100 = 300
E + M = 300 ----------> E + M ONLY = (E + M) - ALL = 300 - 100 = 200

TOTAL = E ONLY + H ONLY + M ONLY + (H+E)ONLY + (H+M)ONLY + (E+M)ONLY + ALL + NONE
2800 = 650 + 550 + 450 + 100 + 300 + 200 + 100 + NONE ----------> 2800 = 2350 + NONE ---------> NONE = 450

1-Difference between English as well as Marathi and English as well as Hindi.
DIFF = (E + M)ONLY - (H + E)ONLY = 200 - 100 = 100

2-Number of members reading atleast 2 newspapers.
TOTAL - (NONE + E ONLY + H ONLY + M ONLY) = 2800 - (450+650+550+450) = 2800 - 2100 = 700

H ONLY + (H + E)ONLY + (H + M)ONLY + ALL = 550 + 100 + 300 + 100 = 1050

H ONLY + M ONLY + E ONLY = 650 + 550 + 450 = 1650

NONE = 450

An advice to you is, atleast for the GMAT, insist on prep material made by trusted sources e.g. Manhattan, Kaplan, Veritas, Magoosh, e-GMAT (only for verbal).

Regards,

Narenn.
_________________
Re: Set Ttheory   [#permalink] 13 Apr 2013, 09:35
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