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210 college students were asked in a survey if they

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210 college students were asked in a survey if they [#permalink] New post 11 Feb 2012, 14:27
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210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?

A. 25
B. 40
C. 50
D. 60
E. 75
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2012, 15:27, edited 2 times in total.
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Re: 800+ [#permalink] New post 11 Feb 2012, 15:26
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210 college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?

A. 25
B. 40
C. 50
D. 60
E. 75

Refer to the diagram below:
Attachment:
Computers.PNG
Computers.PNG [ 5.72 KiB | Viewed 2819 times ]
"One third as many of the students who preferred Mac to Windows, equally preferred both brands" means that 1/3*60=20 equally preferred both brands;

So, we have that 60+20+x+90=210 --> x=40.

Answer: B.
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Re: 210 college students were asked in a survey if they [#permalink] New post 15 Feb 2012, 14:56
How do we know that 60 here represents students who prefer only Mac to Windows and doesn't include the common Part of 20 who prefer both, as when thats the case, the word 'Only' is mentioned otherwise, its assumed, both and Mac to windows is included in the number 60?
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Re: 210 college students were asked in a survey if they [#permalink] New post 15 Feb 2012, 15:08
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arps wrote:
How do we know that 60 here represents students who prefer only Mac to Windows and doesn't include the common Part of 20 who prefer both, as when thats the case, the word 'Only' is mentioned otherwise, its assumed, both and Mac to windows is included in the number 60?


Stem says "60 Students preferred Mac to Windows", so they preferred Mac but not Windows.

Hope it's clear.
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Re: 210 college students were asked in a survey if they [#permalink] New post 15 Feb 2012, 15:17
The questions I have attempted till now when it said :60 Students preferred Mac to Windows, it meant these 60 students included students who preferred Mac to Windows and students who preferred both. And if it did not include both ,it was mentioned as 60 students preferred only Mac to Windows. So got confused. :cry:
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Re: 210 college students were asked in a survey if they [#permalink] New post 15 Feb 2012, 15:41
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arps wrote:
The questions I have attempted till now when it said :60 Students preferred Mac to Windows, it meant these 60 students included students who preferred Mac to Windows and students who preferred both. And if it did not include both ,it was mentioned as 60 students preferred only Mac to Windows. So got confused. :cry:


If it were just "60 Students preferred Mac" then you would be right, but we have "60 Students preferred Mac to Windows", which means that they preferred Mac but not Windows.
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Re: 210 college students were asked in a survey if they [#permalink] New post 15 Feb 2012, 17:03
Makes sense now, Thank You
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Re: 210 college students were asked in a survey if they [#permalink] New post 28 Mar 2012, 11:03
I dint the answer.
This is my approach :

210 = 60+90+x-20( since this is P(AnB)) using the formula (T= P(A) +P(B) - P(AnB) + Neither) , but one of the post show +20 ..

Could you please let me what the mistake is?


Thanks!
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Re: 210 college students were asked in a survey if they [#permalink] New post 28 Mar 2012, 12:09
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kalpanas wrote:
I dint the answer.
This is my approach :

210 = 60+90+x-20( since this is P(AnB)) using the formula (T= P(A) +P(B) - P(AnB) + Neither) , but one of the post show +20 ..

Could you please let me what the mistake is?


Thanks!


I think that you are reading the question in a wrong way.

We are told that "60 Students claimed that they preferred Mac to Windows", which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.

So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.

Refer to the diagram above for correct reading of the question.

Hope it helps.
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Re: 210 college students were asked in a survey if they [#permalink] New post 29 Mar 2012, 07:24
Ya..got it thanks much! :)

These set questions seem to be pretty confusing.. about when to use venn diagram /formulae/ tabular form.

Do we have any standard format for all the set questions?

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Re: 210 college students were asked in a survey if they [#permalink] New post 29 Mar 2012, 07:31
Could you please.. give me one example where we use the formula directly

T = P(a) +P(B) - P(AnB) + Neither of them
200 = 50 +50 - 20 + x (Something like this) -- direct substitution..

Iam getting confused.. bcs each question.. applies the values differently..

Thanks in advance!
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Re: 210 college students were asked in a survey if they [#permalink] New post 29 Mar 2012, 08:06
kalpanas wrote:
Could you please.. give me one example where we use the formula directly

T = P(a) +P(B) - P(AnB) + Neither of them
200 = 50 +50 - 20 + x (Something like this) -- direct substitution..

Iam getting confused.. bcs each question.. applies the values differently..

Thanks in advance!



For this type of 2 good approaches (at least to me!) one is Venn diagram, which Bunuel has explained above and the other is creating a 2*2 matrix- this 1 i prefer more because of number plugging is easy...(refer to the excel file for a little help)... Hope this helps!
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Re: 210 college students were asked in a survey if they [#permalink] New post 29 Mar 2012, 08:19
Expert's post
kalpanas wrote:
Could you please.. give me one example where we use the formula directly

T = P(a) +P(B) - P(AnB) + Neither of them
200 = 50 +50 - 20 + x (Something like this) -- direct substitution..

Iam getting confused.. bcs each question.. applies the values differently..

Thanks in advance!


Check our Questions Banks for all kinds of problems: viewforumtags.php

As for this specific field.
PS questions on overlapping sets: search.php?search_id=tag&tag_id=65
DS questions on overlapping sets: search.php?search_id=tag&tag_id=45

Hope it helps.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: 210 college students were asked in a survey if they [#permalink] New post 16 Apr 2012, 16:06
Oh boy, took me 5 minutes to answer this question, which I didn't think was difficult. Misunderstand the "1/3 times as many" and it messed up my calculations. DOH!

Anyways, just to chime in a little... I see a discussion about Venn Diagram vs. the 2x2 Matrix. If it's any advice to newcomers, the OG Strategy Guides do recommend using the 2x2 Matrix when you have 2 sets of data and the Venn Diagram when you have 3.

Fun question!
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Re: 210 college students were asked in a survey if they [#permalink] New post 17 Apr 2012, 05:33
normally we remember the formula but question tricks us by eliminating common part from single option that is there when formula was deduced solve it through VENN diagram. it is a 30 sec ques.

120 = 60(Mac) + x(Window) + 20(both) => x=40
Re: 210 college students were asked in a survey if they   [#permalink] 17 Apr 2012, 05:33
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