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Set theory question

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Set theory question [#permalink] New post 03 Aug 2009, 02:05
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The table (Please see the attached file) gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
A. 312
B. 336
C. 360
D. 384
E. 420
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Re: Set theory question [#permalink] New post 03 Aug 2009, 04:30
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ankur55 wrote:
The table (Please see the attached file) gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
A. 312
B. 336
C. 360
D. 384
E. 420



IMO it should be A,
See the attached figure.We need to calculate 'A' as shown in figure.

Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312 = The maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time.

Please post the OA.
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untitled.JPG
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Re: Set theory question [#permalink] New post 03 Aug 2009, 05:13
[EDIT - REMOVED BY USER]

Last edited by nplaneta on 17 Jun 2012, 16:43, edited 1 time in total.
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Re: Set theory question [#permalink] New post 03 Aug 2009, 05:25
ankur55 wrote:
nitishmahajan wrote:
ankur55 wrote:
The table (Please see the attached file) gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
A. 312
B. 336
C. 360
D. 384
E. 420


Good explanation Nitish.
Thanks a lot I understood.
By the way can you pls send the formula for Venn diagram mentioning 3 sets.
I really gets confused for 3 sets.
Is the below formula correct?

n(AUBUC)=n(A)+n(B)+n(C)-n(AnB)-n(AnC)-n(BnC)+n(AnBnC)???

IMO it should be A,
See the attached figure.We need to calculate 'A' as shown in figure.

Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312 = The maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time.

Please post the OA.



The formula is right for the union of 3 sets. BTW specifically in this question instead of formulas basic concepts about venn diagrams is more useful. Please check this link http://cnx.org/content/m15203/latest/ might come handy and helpful.

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Re: Set theory question [#permalink] New post 04 Aug 2009, 03:23
Another example with a slight variation :
http://www.beatthegmat.com/sets-any-sho ... 28804.html

We can use appropriate formula based on what information is given. Best is to understand the concept rather than directly applying formula.

nitishmahajan:
Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100. I think this should be:
56 + 42 + 48 - 30 - X - Z - 2Y = 100
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Re: Set theory question [#permalink] New post 04 Aug 2009, 06:43
A...percentof ppl chosen either UF FRT would be 56%+18% = 74%, with 26% not choosing them, assume that these 26% ALL chose bargain prices (26% < 42%), 0.26*1200 = 312
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Re: Set theory question [#permalink] New post 07 Aug 2009, 02:38
req eqn will be => (56-30)+(48-30)+30+x = 100% => hence x = 26% of 1200 = 312...OA A
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Re: Set theory question [#permalink] New post 07 Aug 2009, 07:21
bhushan252 wrote:
req eqn will be => (56-30)+(48-30)+30+x = 100% => hence x = 26% of 1200 = 312...OA A

Hi bhushan,

here x will contain people who fall into "bargain prices only" and "user-friendly"/"FRT + bargain prices". however we are asked to find "bargain prices only". Any comments?
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Re: Set theory question [#permalink] New post 07 Aug 2009, 07:53
can this be solved under 2 mins ? for me to draw the venn diagram and understand itself is taking > 2 mins ..

:(
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Re: Set theory question [#permalink] New post 08 Aug 2009, 21:04
Economist wrote:
bhushan252 wrote:
req eqn will be => (56-30)+(48-30)+30+x = 100% => hence x = 26% of 1200 = 312...OA A

Hi bhushan,

here x will contain people who fall into "bargain prices only" and "user-friendly"/"FRT + bargain prices". however we are asked to find "bargain prices only". Any comments?

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File comment: this is what my defination of x
set representation.GIF
set representation.GIF [ 3.23 KiB | Viewed 9574 times ]


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Re: Set theory question [#permalink] New post 10 Aug 2009, 07:39
bhushan252 wrote:
Economist wrote:

Hi Bhushan, in your figure there are two grey regions. One grey region represents 30.
The other grey region is counted twice as per your formula. correct me if i am wrong. These venn diagrams problems really s**k
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Re: Set theory question [#permalink] New post 15 Jan 2010, 09:56
Bhushan's diagram is correct and so is his solution, If 30 percent of the respondents cited both “user-friendly” and “fast response time, and not bargain prices.. Had the red portion been mentioned it would be just one of the gray regions.
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Re: Set theory question [#permalink] New post 15 Feb 2010, 10:43
nitishmahajan wrote:
ankur55 wrote:
The table (Please see the attached file) gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
A. 312
B. 336
C. 360
D. 384
E. 420



IMO it should be A,
See the attached figure.We need to calculate 'A' as shown in figure.

Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312 = The maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time.
:arrow:
Please post the OA.


Hi nitishmahajan,

I've slight confusion in your solution but I'll appreciate if you rectify my mistake

as per the formula
P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

we've to the bargain price and set theory analytical method.

100 = 56 + 42 + 48 - 30 - P(A n C) – P(B n C) + P(A n B n C)
100 = 116 – P(A n C) – P(B n C) + P(A n B n C)
which in your soln as X+Y+Z but it should be X+Z-Y????

:arrow: By the question stem you mean that "what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time" it is (BP n UF) and (BP n FR)
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Re: Set theory question [#permalink] New post 15 Feb 2010, 11:48
Bullet wrote:
nitishmahajan wrote:
ankur55 wrote:
The table (Please see the attached file) gives three factors to be considered when choosing an Internet service provider and the percent of the 1,200 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
A. 312
B. 336
C. 360
D. 384
E. 420



IMO it should be A,
See the attached figure.We need to calculate 'A' as shown in figure.

Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312 = The maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time.
:arrow:
Please post the OA.


Hi nitishmahajan,

I've slight confusion in your solution but I'll appreciate if you rectify my mistake

as per the formula
P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

we've to the bargain price and set theory analytical method.

100 = 56 + 42 + 48 - 30 - P(A n C) – P(B n C) + P(A n B n C)
100 = 116 – P(A n C) – P(B n C) + P(A n B n C)
which in your soln as X+Y+Z but it should be X+Z-Y????

:arrow: By the question stem you mean that "what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time" it is (BP n UF) and (BP n FR)



I agree with you with the formula here but I am using the basic understanding of the sets here.

Let me try to explain. Consider X, Y, Z as the values only for the area in which it is written.

P(A n C) = X + Y [ A = user friendly and C as Bargain Prices ]

and similarly P( B n C) = Y + Z

If I would have used the formula and then my values would have changed accordingly,

In the question we wanted to calculate the area shown in blue in bottom circle ( marked as required ). Please see the figure and let me know if that helps .
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Re: Set theory question [#permalink] New post 15 Feb 2010, 22:27
nitishmahajan wrote:
Bullet wrote:
nitishmahajan wrote:


IMO it should be A,
See the attached figure.We need to calculate 'A' as shown in figure.

Now as we know 56 + 42 + 48 - 30 - X - Y - Z = 100
116 - ( X + Y + Z )= 100 or 16 = X + Y + Z
From the question stem we also know that X + Y + Z + A = 42 Hence A = 26 %

1200 x 26 /100 = 312 = The maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time.
:arrow:
Please post the OA.


Hi nitishmahajan,

I've slight confusion in your solution but I'll appreciate if you rectify my mistake

as per the formula
P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

we've to the bargain price and set theory analytical method.

100 = 56 + 42 + 48 - 30 - P(A n C) – P(B n C) + P(A n B n C)
100 = 116 – P(A n C) – P(B n C) + P(A n B n C)
which in your soln as X+Y+Z but it should be X+Z-Y????

:arrow: By the question stem you mean that "what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time" it is (BP n UF) and (BP n FR)



I agree with you with the formula here but I am using the basic understanding of the sets here.

Let me try to explain. Consider X, Y, Z as the values only for the area in which it is written.

P(A n C) = X + Y [ A = user friendly and C as Bargain Prices ]

and similarly P( B n C) = Y + Z

If I would have used the formula and then my values would have changed accordingly,

In the question we wanted to calculate the area shown in blue in bottom circle ( marked as required ). Please see the figure and let me know if that helps .



From the above Venn diagram its clear that what you actually wants to find out but can't we get this value using the analytical method (by using formula)

secondly how you calculate this value X + Y + Z + A = 42 ?

Thanks
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Re: Set theory question [#permalink] New post 16 Feb 2010, 02:09
Hi nitishmahajan,

I've slight confusion in your solution but I'll appreciate if you rectify my mistake

as per the formula
P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

we've to the bargain price and set theory analytical method.

100 = 56 + 42 + 48 - 30 - P(A n C) – P(B n C) + P(A n B n C)
100 = 116 – P(A n C) – P(B n C) + P(A n B n C)
which in your soln as X+Y+Z but it should be X+Z-Y????

:arrow: By the question stem you mean that "what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time" it is (BP n UF) and (BP n FR)[/quote]


I agree with you with the formula here but I am using the basic understanding of the sets here.

Let me try to explain. Consider X, Y, Z as the values only for the area in which it is written.

P(A n C) = X + Y [ A = user friendly and C as Bargain Prices ]

and similarly P( B n C) = Y + Z

If I would have used the formula and then my values would have changed accordingly,

In the question we wanted to calculate the area shown in blue in bottom circle ( marked as required ). Please see the figure and let me know if that helps .[/quote]


From the above Venn diagram its clear that what you actually wants to find out but can't we get this value using the analytical method (by using formula)

secondly how you calculate this value X + Y + Z + A = 42 ?

Thanks[/quote]

you can calculate using the formula also,

for the X +Y + Z + A = 42, its mentioned in the question stem, that bargain prices = 42 %
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Re: Set theory question [#permalink] New post 12 Aug 2010, 15:45
alrite.. here is the approach i used to solve this problem..
First convert the percentages to Numbers : 56% of 1200 = 672 --> User Friendly
48% of 1200 = 576 --> Fast Response time
42% of 1200 = 504 --> Bargaining Price

User Friendly and Fast Response time is 30% of 1200 = 360


Kindly refer to the diagram "untitled.jpg" in the previous post by nitishmahajan.. The Required Area 'A' is correctly identified but the 30% area should also include 'Y' That is the shaded Yellow Part plus Y gives the value 360.

Since the yellow shaded area + Y is 360.. the blue shaded area of user friendly + X should be 312 (672-360)

Similarily, the blue shaded area of fast response time + Z should be 216 (576-360).

Since the total number of respondents is 1200,

312(shaded area of + X ) + 360 + 216 (Shaded Area + Z) + A = 1200

A = 1200 - (312+ 360 + 216)

A = 312
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Re: Set theory question [#permalink] New post 28 Nov 2011, 01:13
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SonyGmat wrote:

I wonder why it says maximum possible number of respondents.. People who cited "bargain prices but neither user-friendly nor fast response time will always be 26 % of 1200 or 312.


Is there any chance that they are more or less? Can anyone tell me 1 scenario with different percentages that can meet the information from stem and be different than 312?


It says 'maximum' because the question doesn't say that at least one factor has to be important for each respondent. It is possible that some respondents found none of the factors important. (Say 20% could find 'bargain prices' important while 6% could say that none of the three factors are important.)

Just consider 'user friendly' and 'fast response time' first:
% of people who found one or both of these factors important = 56% + 48% - 30% = 74%
So 26% people find neither 'user friendly' nor 'fast response time' important. This is the maximum % that could find ONLY 'bargain prices important'.
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Re: Set theory question [#permalink] New post 28 Nov 2011, 02:32
VeritasPrepKarishma wrote:
SonyGmat wrote:

I wonder why it says maximum possible number of respondents.. People who cited "bargain prices but neither user-friendly nor fast response time will always be 26 % of 1200 or 312.


Is there any chance that they are more or less? Can anyone tell me 1 scenario with different percentages that can meet the information from stem and be different than 312?


It says 'maximum' because the question doesn't say that at least one factor has to be important for each respondent. It is possible that some respondents found none of the factors important. (Say 20% could find 'bargain prices' important while 6% could say that none of the three factors are important.)

Just consider 'user friendly' and 'fast response time' first:
% of people who found one or both of these factors important = 56% + 48% - 30% = 74%
So 26% people find neither 'user friendly' nor 'fast response time' important. This is the maximum % that could find ONLY 'bargain prices important'.


Thanks for the explanation Karishma.

I assumed that there wasn't such an option because there were 3 factors cited in the table.
Re: Set theory question   [#permalink] 28 Nov 2011, 02:32
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