Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 08 Feb 2016, 11:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Set theory question

Author Message
TAGS:
Manager
Joined: 06 May 2009
Posts: 76
Followers: 2

Kudos [?]: 37 [0], given: 3

Set theory question [#permalink]  03 Aug 2009, 02:05
3
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

67% (00:00) correct 33% (01:38) wrong based on 14 sessions
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
Attachments

table.JPG [ 17.59 KiB | Viewed 10581 times ]

Senior Manager
Joined: 25 Jun 2009
Posts: 306
Followers: 2

Kudos [?]: 100 [2] , given: 6

Re: Set theory question [#permalink]  03 Aug 2009, 04:30
2
KUDOS
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.

Attachments

untitled.JPG [ 26.99 KiB | Viewed 10516 times ]

Intern
Status: Applying
Joined: 30 Jul 2009
Posts: 39
Followers: 0

Kudos [?]: 4 [0], given: 3

Re: Set theory question [#permalink]  03 Aug 2009, 05:13
[EDIT - REMOVED BY USER]

Last edited by nplaneta on 17 Jun 2012, 16:43, edited 1 time in total.
Senior Manager
Joined: 25 Jun 2009
Posts: 306
Followers: 2

Kudos [?]: 100 [0], given: 6

Re: Set theory question [#permalink]  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.

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.

Cheers
Director
Joined: 01 Apr 2008
Posts: 898
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 20

Kudos [?]: 443 [0], given: 18

Re: Set theory question [#permalink]  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
Senior Manager
Joined: 17 Jul 2009
Posts: 299
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Followers: 1

Kudos [?]: 38 [0], given: 9

Re: Set theory question [#permalink]  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
Manager
Joined: 18 Jul 2009
Posts: 169
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 77 [0], given: 37

Re: Set theory question [#permalink]  07 Aug 2009, 02:38
req eqn will be => (56-30)+(48-30)+30+x = 100% => hence x = 26% of 1200 = 312...OA A
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Director
Joined: 01 Apr 2008
Posts: 898
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 20

Kudos [?]: 443 [0], given: 18

Re: Set theory question [#permalink]  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?
Manager
Joined: 07 Apr 2009
Posts: 145
Followers: 1

Kudos [?]: 10 [0], given: 3

Re: Set theory question [#permalink]  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 ..

Manager
Joined: 18 Jul 2009
Posts: 169
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 77 [0], given: 37

Re: Set theory question [#permalink]  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?

Attachments

File comment: this is what my defination of x

set representation.GIF [ 3.23 KiB | Viewed 10310 times ]

_________________

Bhushan S.
If you like my post....Consider it for Kudos

Director
Joined: 01 Apr 2008
Posts: 898
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 20

Kudos [?]: 443 [0], given: 18

Re: Set theory question [#permalink]  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
Manager
Joined: 25 Aug 2009
Posts: 175
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 11

Kudos [?]: 143 [0], given: 3

Re: Set theory question [#permalink]  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.
_________________

Rock On

Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 67 [0], given: 9

Re: Set theory question [#permalink]  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.

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????

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)
_________________

--Action is the foundational key to all success.

Senior Manager
Joined: 25 Jun 2009
Posts: 306
Followers: 2

Kudos [?]: 100 [0], given: 6

Re: Set theory question [#permalink]  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.

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????

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 .
Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 67 [0], given: 9

Re: Set theory question [#permalink]  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.

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????

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
_________________

--Action is the foundational key to all success.

Senior Manager
Joined: 25 Jun 2009
Posts: 306
Followers: 2

Kudos [?]: 100 [0], given: 6

Re: Set theory question [#permalink]  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????

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 %
Intern
Joined: 05 Jul 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Set theory question [#permalink]  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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6219
Location: Pune, India
Followers: 1676

Kudos [?]: 9598 [1] , given: 197

Re: Set theory question [#permalink]  28 Nov 2011, 01:13
1
KUDOS
Expert's post
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'.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 23 Oct 2011
Posts: 84
Followers: 0

Kudos [?]: 45 [0], given: 34

Re: Set theory question [#permalink]  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
Similar topics Replies Last post
Similar
Topics:
number theory good question 1 26 Mar 2011, 23:04
2 4 question set 5 05 May 2010, 13:45
Sets and percentages question 1 03 Jan 2010, 08:59
6 Set of three PS questions 15 13 Oct 2009, 19:10
Display posts from previous: Sort by

# Set theory question

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.