swerve wrote:48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?
A. 19.5%
B. 21.5%
C. 20%
D. 18.5%
E. 17.5%
Use the following DOUBLE- MATRIX to organize the data:
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N.
Let x = the number of who used both M and N, implying that the number who used neither M nor N = 48-x.
The following matrix is yielded:
44% of respondents did not use M.
39% used N.
The following matrix is yielded:
What percent of respondents used only N?
Let y = the percent who used only N.
The following matrix is yielded:
Since the top row must sum to 39, and the middle column must sum to 44, the following equations are implied:
x + y = 39
y + (48-x) = 44.
Adding together the two equations, we get:
x + y + y + 48 - x = 39 + 44
2y + 48 = 83
2y = 35
y = 17.5.
The correct answer is
E.
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