Another "hard one" from GMAT PREP, please help

[Crack_Mat]

Originally Posted by tomintampa

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

...

If 30 percent of the respondents cited both “user-friendly” and “fast response time”,

A = only User-friendly (UF)
B = only Fast response (FR)
C = Bargain prices (BP)

P = only (UF + FR)
Q = only (FR + BP)
R = only (UF + BP)

Z = All three

T = none = assume 0 in order to maximize the response!
So A+B+C+P+Q+R+Z = 100--(0)

Also 30 = P+Z (please focus on wordings, 30% cited both UF and FR, it does include some who marked BP also (that is Z))

Now just imagine a van-diagram:
A+P+Q+Z = 56--(1)
B+P+Q+R = 48--(2)
C+Q+R+Z = 42--(3)
and P+Z = 30---(4)

add 1,2,3 and put value from (0) and (4)
you get 2Q+R= 16--(5)
Put (5) into (3)
you get
C = 26 - (Z-Q);
Now for maximum of C, Z - Q must be zero, that mean those voting for only (A and C) must be equal to those voting to all, and that is possible!

so C = 26%
sp 12*26 = 312!

[Crack_Mat]

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

Another approach could be:
Those Marked UF = 56
Those Marked FR = 48

Those marked both = 30

So % of those (who marked UF + who marked FR) = those marked any of UF or FR = 56+48-30 = 74 (-30 as it being count in UF and FR twice)

So We know how many marked either of UF and FR. They may have those who also marked BP also.

Only BP = not of those (who voted for either)
= 100 -74 = 26
so 26% 0f the 1200 = 312

its a kind of explanation of Sandy's response.

[Crack_Mat]

I think sandy's solution is most elegant one!!!

[sannddyy]

Hi fokes,

I think solving it this way would be easier.

30% of total = 360(number of people who vote for both user friendly and fast responce time)

number of people who voted for user friendly = 56%=672
number of people who voted for Fast response time = 48%=576

Among these people there are 360 people who have voted for both. If we assume that 360 people who has voted for user fiendly (out of 672) had also voted for Fast response time, then the total number of people who voted for one of the two or both of them becomes 888(672+216). 1200- 888 gives the required answer 312.

[desret man]

Hi ,
The easyest way to answer this question
User-friendly 56% => 672
Fast response time 48% => 576
Bargain prices 42% => 504
To find the maximum possible number of respondents for c, we can assume that all who responded for c are not choose a or b
so == > 1200 - ( 672 + 576 - 360 ) = 312
another way to answer is = 1 - ( .56 + .48 - .3 )= .26 * 1200 = 312
answer a
I hope its helpful and my logic is correct

[sksgill]

Originally Posted by 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

what if the question were reversed to find the minimum for bargain prices only?