praveengmat wrote:

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

Actually this question is easier than it seems to be:

Let's say we have 100 people, :

56 cited "User-friendly";

48 cited "Fast response time";

42 cited "Bargain prices";

Also 30 cited BOTH “user-friendly” and “fast response time”.

Question is: what is the maximum possible number of respondents who cited

ONLY "bargain prices"?

The group who cited “user-friendly” OR “fast response time” has U+F-U&F=56+48-30=74 people;

As there are total of 100 people hence there are 100-74=26 people who cited

neither “user-friendly” nor “fast response time”. Could all these 26 people cited "bargain prices"? As "bargain prices"=42>26, so YES.

So max possible # of people who cited

ONLY "bargain prices" is 26, or transforming it back to the percents 26% --> 1200*26%=312.

Answer: A.

mainhoon wrote:

Ok, so in this case we want to maximize the set B (no overlap with U and F). Now, the number of people that belong to U or F = U + F - (UandF). Let me take a total set of 100 (reduce from 1200). Then U or F = 56 + 48 - 30 = 74. That leaves us with 100-74 = 26. In terms of 1200, then 26 x 12 = 312. That is (A). But I don't understand how B is 42%? This is confusing.

We've got that 42 cited "Bargain prices" and 26 cited

ONLY "Bargain prices", so 42-26=16

ALSO cited either “user-friendly” or “fast response time” (or both).

Hope it helps.

How do we know that there are no respondents who marked none of the 3 factors as important? In that case, the union won't be equal to 1200.

Shouldn't the question have mentioned clearly that the respondents mark atleast one of the factors as important?