The table gives three factors to be considered when choosing

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.

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

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

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

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".


 

­I draw the union of 3 circle like this but I can't make the table.

Let's define some variables first.
"user-friendly" = A = 56
"fast response time" = B = 48
"bargain prices" = C =42
"user-friendly" and "fast response time" = D = 30
"user-friendly" and "bargain prices" = E
"fast response time" and "bargain prices" = F
"All Three" = G
To work with overlapping sets you can use the following formula

A+B+C-D-E-F-2G+Neither = 100% , but since they are asking you for a Max quantity you should asume that you have zero in the "Neither" group so you end with the following

56+48+42-30-E-F-2g=100
E-F-2G=16
Since E-F-2G represents the amount of "bargain prices" (C) That it's shared with other sets you only to rest this percentage with the amount of the entire C set to know the percentage that ONLY select "bargain prices"

42%-16% = 26%, And 26% of 1200 = 312.­

this explanation video by KarishmaB 's helped me to crack this one
https://www.youtube.com/watch?v=oLKbIyb1ZrI

Bunuel

are there more questions like this one please? how do I know that i can assume its out of 100 and solve like that? thanks so much

ExpertsGlobal kindly solve this problem

Hi, hope this helps

As per the ques stem, total is 100 % i.e 1200
in which
U(user friendly)=56% or a+d+e+g=56% =>a=56-30-e-g
F(Fast Response)=48% or b+d+g+f=48%=>b=48-30-g-f
B(Bargain price)=42% or c+e+f+g=42%=>c=42-e-f-g
U&F=30% or d=30%

We need to find only c i.e 42-e-f-g=c

Now, a+b+c+d+e+f+g=100
26-g-e+18-g-f+42-e-g-f+d+e+f+g=100
86-g-g-e-f+30=100
116-2g-e-f=100
2g+e+f=16

we can also write g+e+f=42-c

g+42-c=16

since, max possible value of c can be possible if g is 0, then

c=42-16=26,(remember this 26 is in percentage),

hence c=26%*1200= 312

When you say that te group that cited U or F is 56 + 48 -30 (U + F - both) you are asumming that there are not people who cited three, is that right ?

No. The 74% who cited “user-friendly” OR “fast response time” (or both) also includes those who cited "bargain prices." As discussed, the maximum possible number of people who cited ONLY "bargain prices" is 26%, which means that in this case, 42% - 26% = 16% of respondents cited "bargain prices" along with either “user-friendly” or “fast response time” (or both). So, those 16% are part of the 74% group.

Let's assume that the overlapping part is X, Y, Z, A(overlap with U F and B).
In order to max only B. we need to minimize X, Y, Z, A.
X+Y+Z+A= (672+576+504)-1200=552
We know that X+A=30%*1200= 360
552-360= 192 = Y+Z
To Max only B, Min A=0
1200*42%=504
504-192=312

So we know that

b+f = 26%

Also, a+d = 18%

How did you deduce this?