Problem Solving

table attached
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 think should be A.

pandeyvineet24 wrote:i think should be A.

any reason why u think so

Let's have "user friendly" = UF
"fast response time" = FRT
"bargain prices" = BP

We know that "30 percent of respondents are both UF and FRT". That comes out to 360.

We are also told the percentage values for those people who either responded just for UF or FRT, or for both UF and FRT.

UF = 1,200 * .56 = 672
FRT = 1,200 * .48 = 576

Subtract our "both UF and FRT" number from each of these and you'll get:

Only UF = 672 - 360 = 312
Only FRT = 576 - 360 = 216

Since we want to maximize the number of people who listed BP as their main concern we need to subtact the sum of "only UF, only FRT, and both UF and FRT" from our total number:

1,200 - 312 - 216 - 360 = 312

I think A is the answer. What's the OA?

antondesh wrote:Let's have "user friendly" = UF
"fast response time" = FRT
"bargain prices" = BP

We know that "30 percent of respondents are both UF and FRT". That comes out to 360.

We are also told the percentage values for those people who either responded just for UF or FRT, or for both UF and FRT.

UF = 1,200 * .56 = 672
FRT = 1,200 * .48 = 576

Subtract our "both UF and FRT" number from each of these and you'll get:

Only UF = 672 - 360 = 312
Only FRT = 576 - 360 = 216

Since we want to maximize the number of people who listed BP as their main concern we need to subtact the sum of "only UF, only FRT, and both UF and FRT" from our total number:

1,200 - 312 - 216 - 360 = 312

I think A is the answer. What's the OA?

Not sure how you did it ? when i draw 3 venns intersecting each other, i do not see how your solution seperates all unnecessary 6 groups to get the desired group ?

It would be great if you can draw it.

Here you go... quick and dirty.

Hope this helps

I got 312 too. What is the OA??

hi is the 54% stated in mainproblem under bp of no signifiance?

antondesh wrote:Here you go... quick and dirty.

Hope this helps

are you sure you can assume all yellow portion is 0. I get 312 but by assuming that only the middle segment (the area in common with all three) is 0 and the other 2 yellow segments total 16%.
Am I missing something. Pls let me know if you think the attached venn diag is incorrect.