Another "hard one" from GMAT PREP, please help

[tomintampa]

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

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 dont remember the answer

[iceman0]

Here is my take

User-friendly = A
Fast response time = B
Bargain prices = C

A+B+C=1200

672+576+504-any two + all three + none=1200 ==> -any two + all three + none=-552

(A and B)=360
any two=(A and B)+(B and C)+(A and C)

C=504-(B and C)-(A and C) ==>You need to minimize (B and C)+(A and C) to maximize C

-360 -(B and C)-(A and C) + all three + none=-552
-(B and C)-(A and C) + all three + none=-192 ==> To minimize (B and C)+(A and C) you make all three and none cero

(B and C)+(A and C)=192

C=504-192
C=312

[sandy_online]

% of user- friendly and fast response time = 56% + 48% - 30% = 74%
%of only bargain prices = 100-74 = 26%
total number = 1200*26/100 = 312

[Danagmat]

Hi can someone explain in details, Sandy's answer

thanks
dana

[wanderwanderer]

Please explain this again.

Thanks

[benadil]

guys you need to draw morgans diagram to solve this type of questions if you do you will understnd easily his answer
draw three circles each representing the percentage or number of answers for each criterion the circles intersect with each other
i think after that you will understand his answer

[clock60]

Originally Posted by tomintampa

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

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 dont remember the answer

one more way to solve the problem. But i am not sure that it is completely correct.
at first let us introduce the following symbols
a-friendly only
b-fast response only
c-prices only
y-friendly+responce only
x-prices+friendly only
z-prices+fast responce only
w-all three
by definition
a+b+c+x+y+z+w=100%
so according our condition
a+x+y+w=56%
b+y+z+w=48%
c+x+z+w=42%
and given that frienfly+fast responce=30%
in our symbol it is y =30%
insert y in all 4 equation to get rid off
a+b+c+x+z+w=70 (2)
a+x+w=26
b+z+w=18
c+x+z+w=42
add all three above equation
a+b+c+2x+2z+3w=86 (1)

then let us substract (1)-(2) so we have
x+z+2w=16
we don not forget that our aim is to find
bargain prices only in our way it is c
c+x+z+w=42 (3)
x+z+2w=16 (4)
substact (3)-(4)
c-w=26
i think in order c to be max w must be min so w=0 (but it is only my admission and i think weak point in all solution)
it could be easier to solve if we knew from the problem that nobody is satisfied with all three
any way w=0
so c=26
26%from 1200=312
so A
any responses about correctness this aproach will be highly appreciated

[bretania]

Clock60,

My concern about this solution is this:

Because this condition in the problem (If 30 percent of the respondents cited both “user-friendly” and “fast response time”), does not include the word "only", could this statement/condition then also mean that this 30% include some respondents who picked all 3 factors as important?

In this case, then perhaps we need a different set of variables to show this? Meaning, this 30% could be your W+Y?

Is the wording of the problem by the way accurate?

[bretania]

Another one, clock60, I think you're right about making w zero in order to maximize the "only prices" people.

[clock60]

Originally Posted by bretania

Clock60,

My concern about this solution is this:

Because this condition in the problem (If 30 percent of the respondents cited both “user-friendly” and “fast response time”), does not include the word "only", could this statement/condition then also mean that this 30% include some respondents who picked all 3 factors as important?

In this case, then perhaps we need a different set of variables to show this? Meaning, this 30% could be your W+Y?

Is the wording of the problem by the way accurate?

absolutely agree with you. the problem is in wording i hesitated between including or not. with including all three the prob even simplier