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Set theory question .... Please help !!!!!

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Set theory question .... Please help !!!!! [#permalink] New post 18 May 2010, 06:40
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43% (05:16) correct 57% (04:20) wrong based on 8 sessions
In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then,

The ratio of number of students who like only coffee to the number who like only tea is
a) 5:3
b) 8:9
c) 2:3
d) 3:2
e) None of these

Hello Guys... I am not able to figure out the % of people who didi all three. Help please .....
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Re: Set theory question .... Please help !!!!! [#permalink] New post 18 May 2010, 19:31
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C

We need to write down equation for Vienn Diagram:

100% = 48% + 54% + 64% - 28% - 32% - 30% + t + 6% = 100%
where t - % of students who drink tea and coffee, and smoke.

From the equation:
t = 18%

Now, let's find our ratio:

ratio = (48% - 28% - 30% + 18%)/(54% - 28% - 32% + 18%) = 8%/12% = 2/3
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Re: Set theory question .... Please help !!!!! [#permalink] New post 19 May 2010, 06:44
Thanks Walker ... I understood the explanation.

One question though.....
For instance , in this question 28% liked coffee and tea. Does this mean that 28 % liked ONLY coffee and tea ?

I am assuming that since 28 % liked coffee and tea and some % (say x%) like all three things ( coffee, tea and smoke), then to get ONLY coffee and tea % we have to subtract x% from 28 % .Then to get ONLY coffee % , we have to subtract (28 - x) from 48 %.

I have solved couple of questions in which similar statements were given and I had to subtract in the way I mentioned to get the correct answer.

Hope I make sense... Please resolve my confusion.

Thanks,
V
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Re: Set theory question .... Please help !!!!! [#permalink] New post 19 May 2010, 07:05
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I think "like coffee and tea" doesn't mean only coffee and tee.

vineet474 wrote:
...I am assuming that since 28 % liked coffee and tea and some % (say x%) like all three things ( coffee, tea and smoke), then to get ONLY coffee and tea % we have to subtract x% from 28 % .Then to get ONLY coffee % , we have to subtract (28 - x) from 48 %.


48% - coffee
(28% - x%) - only coffee and tee
(30% - x%) - only coffee and smoke
x% - coffee, tea and smoke

only coffee = coffee - only coffee and tee - only coffee and smoke - coffee, tea and smoke

only coffee = 48% - (28% - x%) - (30% - x%) - x% = 48% - 28% - 30% + x%

I hope it helps.
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Re: Set theory question .... Please help !!!!! [#permalink] New post 19 May 2010, 22:10
Hey...I got it now. :-D

Thanks a lot Walker... Appreciate your help.

I am trying to finish quant since I have 2 weeks off from work. Will trouble you guys again if I have any doubts.

Please bare !! :wink:

Any advice on how to approach RC. To be honest, I am very weak in RC and whenever I try to start it, I either loose focus or something comes up to take me away from it. In my opinion, you just cannot rely on SC and CR. In order to get a decent verbal score, you must get your RC questions right.(not all, but a fair percentage so to speak).

I have read few RC posts on this forum in which writing notes of ONLY first paragraph and then taking key words from the rest of them is one of the strategy employed. Is this the way I should approach RC ?

Please advice.

Thanks,
V
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Re: Set theory question .... Please help !!!!! [#permalink] New post 20 May 2010, 03:20
Expert's post
There is a lot of thoughts about the best RC strategy. I've improved my RC success rate dramatically just by reading slowly with huge interest and solving SC faster to have enough time for RC.

Here are my thoughts: help-nedded-how-to-excel-in-reading-comprehension-82600.html?view-post=620252#p620252

Also take a look at: new-to-the-verbal-forum-please-read-this-first-77546.html
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Re: Set theory question .... Please help !!!!! [#permalink] New post 16 Dec 2010, 16:40
I have tried to solve this problem by using real numbers rather than percents and I got confused.

48% (960) likes coffee
54% (1080) likes tea
64% (1280) smokes
6% (120) neither
28% (560) likes coffee and tea
32% (640) smokes and likes tea
30% (600) smokes and likes coffee

2000 (total) = 960 (coffee) + 1080 (tea) + 1280 (smoking) -560(coffee & tea) - 640 (smoking & tea) - 600 (smoking & coffee) + X (coffe & tea & smoking) +120 (neither)
X=360

From the V.Diagram I got
To calculate ONLY coffee can I add coffe&tea and coffee&smoking substract coffee&tea&smoking and substract it from coffee total(960) ???
ONLY COFFEE 160
ONLY TEA 240
ONLY SMOKING 400

160/240= 2/3
Re: Set theory question .... Please help !!!!!   [#permalink] 16 Dec 2010, 16:40
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