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The table gives three factors to be considered when choosing

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praveengmat
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The table gives three factors to be considered when choosing [#permalink] New post   Updated on: 27 Jul 2023, 04:45
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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"?

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

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Originally posted by praveengmat on 11 Aug 2010, 11:49.
Last edited by Bunuel on 27 Jul 2023, 04:45, edited 3 times in total.
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Re: The table gives three factors to be considered when choosing [#permalink] New post   12 Aug 2010, 03:54
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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?”



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] New post   11 Aug 2010, 18:33
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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] 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] 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] New post   25 Sep 2013, 01:35
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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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Re: The table gives three factors to be considered when choosing [#permalink] New post   11 Jan 2018, 08:52
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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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Re: The table gives three factors to be considered when choosing [#permalink] New post   05 Feb 2019, 12:19
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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"?


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


I got the answer without fully understanding how I got it. Could someone explain what I did right/what I did wrong?

To maximize the # of people who only cited bargain prices we need to assume the number of people who cited bargain prices + 1 other factor to be 0.

So we have 56% User Friendly (UF), 48% Fast time (F), 42% Bargain prices (b)

We also know that UF&F = 30. We, however, do not know B&UF&F. We can make this value the lowest when we assume B&UF and B&F to be 0.

So 56 + 48 + 42 - 30 - all three = 100
all three = 16

42 - 16 = 26%

26% of 1200 = 312 (answer choice A)

My question is in the last part. Typically you subtract 2 * all three since it is counted 3 times. But when I do that I get all three = 8% which gives me an answer of 408. In this case why do we do what we did above or If I got the answer coincidentally, what did I do wrong here?
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Re: The table gives three factors to be considered when choosing [#permalink] New post   31 Mar 2024, 16:54
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NinetyFour 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"?


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

I got the answer without fully understanding how I got it. Could someone explain what I did right/what I did wrong?

To maximize the # of people who only cited bargain prices we need to assume the number of people who cited bargain prices + 1 other factor to be 0.

So we have 56% User Friendly (UF), 48% Fast time (F), 42% Bargain prices (b)

We also know that UF&F = 30. We, however, do not know B&UF&F. We can make this value the lowest when we assume B&UF and B&F to be 0.

So 56 + 48 + 42 - 30 - all three = 100
all three = 16

42 - 16 = 26%

26% of 1200 = 312 (answer choice A)

My question is in the last part. Typically you subtract 2 * all three since it is counted 3 times. But when I do that I get all three = 8% which gives me an answer of 408. In this case why do we do what we did above or If I got the answer coincidentally, what did I do wrong here?

NinetyFour  I believe the issue is a subtle reading trap on these: the 30% that you put for "both UF&F" could also be distributed into the B&UF&F region. In other words, when the wording in the passage says "20% have both X and Y", some of those 20% could also have Z. 

I recommend keeping it simple with Bunuel's solution here; we don't need to know what's distributed into every single area (it's not necessary to use an equation that includes the "All Three"), we just need to find the max for "only bargain prices".


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