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?”
A. 312
B. 336
C. 360
D. 384
E. 420
Actually, this question is easier than it seems. Let's say we have 100 people:
- 56 cited "User-friendly".
- 48 cited "Fast response time".
- 42 cited "Bargain prices".
Additionally, 30 cited BOTH “user-friendly” and “fast response time”.
The 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 - Both = 56 + 48 - 30 = 74 people.
Since there are a total of 100 people, there are 100 - 74 = 26 people who cited
neither “user-friendly” nor “fast response time”. Could all these 26 people have cited "bargain prices"? Since "bargain prices" = 42 > 26, the answer is YES.
So, the maximum possible number of people who cited
ONLY "bargain prices" is 26, or transforming it back to percentages: 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 established that 42 people cited "Bargain prices," and among them, 26 cited
ONLY "Bargain prices." Therefore, 42 - 26 = 16
ALSO cited either “user-friendly” or “fast response time” (or both).
Hope it helps.