venn D

vipulgoyal 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

Let:
U = user-friendly
F = fast-response time
B = bargain prices
UF = user-friendly and fast-response time
BU = bargain prices and user-friendly
BF = bargain prices and fast-response time
BUF = all 3 groups.

If we subtract the percentage for UF -- 30% -- from the percentages for the 3 groups, we get:
(56+48+42) - 30 = 116%.
Implication:
Since the total must be 100%, at least 16% must belong to BU, BF or BUF.

Since 42% belong to B, and at least 16% belong to BU, BF, or BUF, the greatest percentage who could belong to ONLY B = 42-16 = 26%.
Thus, the maximum value of Only B = 0.26(1200) = 312.

The correct answer is A.

vipulgoyal 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



The OA is A but with the line method I am getting B

Please open the word document attached.