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The table gives three factors to be considered when choosing

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The table gives three factors to be considered when choosing  [#permalink]

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New post Updated on: 23 Feb 2016, 13:07
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The table 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"?
Image

A. 312
B. 336
C. 360
D. 384
E. 420

Attachment:
table.JPG
table.JPG [ 15.63 KiB | Viewed 16014 times ]

Originally posted by praveengmat on 11 Aug 2010, 11:49.
Last edited by Bunuel on 23 Feb 2016, 13:07, edited 2 times in total.
Edited the question
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The table gives three factors to be considered when choosing  [#permalink]

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New post 12 Aug 2010, 03:54
11
15
praveengmat wrote:
The table 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?”

Image

A. 312
B. 336
C. 360
D. 384
E. 420


Actually this question is easier than it seems to be:

Let's say we have 100 people, :
56 cited "User-friendly";
48 cited "Fast response time";
42 cited "Bargain prices";

Also 30 cited BOTH “user-friendly” and “fast response time”.

Question is: what is the maximum possible number of respondents who cited ONLY "bargain prices"?

The group who cited “user-friendly” OR “fast response time” has U+F-U&F=56+48-30=74 people;

As there are total of 100 people hence there are 100-74=26 people who cited neither “user-friendly” nor “fast response time”. Could all these 26 people cited "bargain prices"? As "bargain prices"=42>26, so YES.

So max possible # of people who cited ONLY "bargain prices" is 26, or transforming it back to the percents 26% --> 1200*26%=312.

Answer: A.

mainhoon wrote:
Ok, so in this case we want to maximize the set B (no overlap with U and F). Now, the number of people that belong to U or F = U + F - (UandF). Let me take a total set of 100 (reduce from 1200). Then U or F = 56 + 48 - 30 = 74. That leaves us with 100-74 = 26. In terms of 1200, then 26 x 12 = 312. That is (A). But I don't understand how B is 42%? This is confusing.


We've got that 42 cited "Bargain prices" and 26 cited ONLY "Bargain prices", so 42-26=16 ALSO cited either “user-friendly” or “fast response time” (or both).

Hope it helps.
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 11 Aug 2010, 18:33
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1
praveengmat wrote:
The table 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?”
User-friendly 56%
Fast response time 48%
Bargain prices 42%
A. 312 B. 336 C. 360 D. 384 E. 420



Took some time to get to the correct answer.

Answer - A (312)

Given details in the question stem.
Total - 1200, User-Friendly - 672, Fast response time - 576, Bargain price - 504.


Let the sum of user friendly & fast response and bargain price be A.
And the overlap between the user friendly and bargain price be X, overlap between fast response and bargain be Y.
Derived details.
Overlapped area between User-Friendly & Fast response time - (360 - A).
User-Friendly alone -- (672 - 360 - A - A - X) -- (312 - 2A - X).
Fast response time -- (576 - 360 - A - A -Y) -- (216 - 2A - Y).
Bargain -- (504 - 360 - A - X - Y) -- (144 - A - X- Y)

Hence the total is
(312 - 2A - X) + (216 - 2A - Y) + (144 - A - X - Y) + (360 - A) + A + X + Y = 1200

-- -5A - X - Y = 168

We know that the bargain alone (without fast response and user friendly) is 144 - A - X - Y.

Hence 144 - 4A - A - X - Y => 144 - 4A + 168

- 312 - 4A. Since we need to maximize the bargain portion take A as zero.

Hence the area under bargain is 312.
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 25 Nov 2011, 17:13
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


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?
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 03 Feb 2012, 04:07
SonyGmat 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


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?


I merged your question to the earlier discussion of the same problem. Please refer to the solution above and ask if anything remains unclear.

Hope it helps.
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 22 Aug 2012, 02:07
Such type of logic based set questions are easy to solve using Venn diagram than using formula as it is easy to visualize in venn diagrams.

Give it a try using venn diagram, i am sure it will take much less time
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 11 Feb 2013, 19:59
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Breakdown as follows: 672(UF), 576(FRT), 504(BP). For a total of 1752. Since 30% (360 ppl) like both UF & FRT we need to subtract 360 from the 1752 total. This leaves us with 1392. Now since 504 people like BP and we know that some ppl like both BP and one of the others, we need to determine the maximum # of ppl who like only BP. To maximize only BP, we need to account for the total difference between 1392 and 1200 (the total number of ppl surveyed). This leaves us with 192. Therefore, of the 504 ppl who like BP the maximum # of ppl who could like only BP is 504-192 = 312. Answer: A
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 11 Feb 2013, 22:49
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So we know that

b+f = 26%

Also, a+d = 18%

Now,

a+d+b+f+g+e=(26+18+30)% = 74%

Thus, c = (100-74)% = 26%

Thus, c = 26*12 = The only option ending with a 2(as units digit)

A.
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 25 Sep 2013, 01:35
Bunuel wrote:
praveengmat wrote:
The table 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?”

User-friendly 56%
Fast response time 48%
Bargain prices 42%

Hope it helps.


Hi Bunuel

to increase my understanding I changed the bargain price value:

Bargain prices 24% (actual value is 42%)

then in percentages would the answer be 24% since 24%<26%? and would the venn diagram be the one I have attached?

PS: I am very bad in Set :(
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Venn Diag.jpg [ 41.1 KiB | Viewed 11752 times ]

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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 19 Nov 2013, 09:01
Bunuel wrote:
praveengmat wrote:
The table 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?”

User-friendly 56%
Fast response time 48%
Bargain prices 42%

A. 312
B. 336
C. 360
D. 384
E. 420


Actually this question is easier than it seems to be:

Let's say we have 100 people, :
56 cited "User-friendly";
48 cited "Fast response time";
42 cited "Bargain prices";

Also 30 cited BOTH “user-friendly” and “fast response time”.

Question is: what is the maximum possible number of respondents who cited ONLY "bargain prices"?

The group who cited “user-friendly” OR “fast response time” has U+F-U&F=56+48-30=74 people;

As there are total of 100 people hence there are 100-74=26 people who cited neither “user-friendly” nor “fast response time”. Could all these 26 people cited "bargain prices"? As "bargain prices"=42>26, so YES.

So max possible # of people who cited ONLY "bargain prices" is 26, or transforming it back to the percents 26% --> 1200*26%=312.

Answer: A.

mainhoon wrote:
Ok, so in this case we want to maximize the set B (no overlap with U and F). Now, the number of people that belong to U or F = U + F - (UandF). Let me take a total set of 100 (reduce from 1200). Then U or F = 56 + 48 - 30 = 74. That leaves us with 100-74 = 26. In terms of 1200, then 26 x 12 = 312. That is (A). But I don't understand how B is 42%? This is confusing.


We've got that 42 cited "Bargain prices" and 26 cited ONLY "Bargain prices", so 42-26=16 ALSO cited either “user-friendly” or “fast response time” (or both).

Hope it helps.


Hi Bunuel,

How do we know that there are no respondents who marked none of the 3 factors as important? In that case, the union won't be equal to 1200.

Shouldn't the question have mentioned clearly that the respondents mark atleast one of the factors as important?

Thanks,
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Re: The table gives three factors to be considered when choosing  [#permalink]

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New post 19 Jun 2016, 07:23
The method of sets is exactly what I used. Labeling the individual areas always works for me.
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The table gives three factors to be considered when choosing  [#permalink]

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New post 11 Jan 2018, 08:52
N (Either "user-friendly" or "fast response time" or both) = N (user friendly) + N (fast response time) - N(both) = 56 + 48 - 30 = 74

N (Either "user-friendly" or "fast response time" or both)
|------------74------------------------>--26----|

|------------58---------------<--------42-------| N (bargain prices)

from above, min overlap between N(Either "user-friendly" or "fast response time" or both) and N(bargain prices) is 16
|------------58--------------<-16--><-26---->| N (bargain prices)

so max (bargain prices neither user-friendly" nor "fast response time) = 26%
so max = (26/100) * 1200 = 312
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