Problem Solving

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

total number of resp = 1200 = n
X = N(BF - NF - FRT)
N (Uf) + N (FRT) - N (uf and FRT) + X = n
==> 0.56n + 0.48n - 0.3n + X = n
=> n = 0.26n = 0.26 * 1200 = 312
Hence A

akdayal wrote:total number of resp = 1200 = n
X = N(BF - NF - FRT)
N (Uf) + N (FRT) - N (uf and FRT) + X = n
==> 0.56n + 0.48n - 0.3n + X = n
=> n = 0.26n = 0.26 * 1200 = 312
Hence A

thank you.. but i am little bit confused ....explain me clearly please...........

We have been provided with total percentage of User friendly option and of fast response option as such
56+42-30 is sum of percentage of people opting for User friendly and fast response options (it includes people opting for any two of the given three choices and all three of the given choices; leaving out only the people opting for the bargain prices, can be seen in the venn diagram.)

Hence 100-(56+42-30) gives exact percentage of people opting for bargain prices only and not user friendly nor fast response.

i.e. 24%

and 24% of 1200 = 312 ans.!!!