BTGmoderatorDC wrote:When 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
A. 11/14
B. 13/18
C. 4/7
D. 3/7
E. 3/14
OA A
Source: Official Guide
Fraction of votes in favor of the counted votes = 2/9 * 3/4 = 1/6;
Thus, fraction of votes against the counted votes = 2/9 - 1/6 = 1/18;
Remaining uncounted votes = 1 - 2/9 = 7/9;
Say x is the fraction of uncounted votes that must be against the resolution of the uncounted votes so that the total count will result in a vote of 2 to 1 against the resolution
Fraction of votes that must be against of the uncounted votes = 7/9*x = 7x/9;
Thus, fraction of votes that must be favor of the uncounted votes = 7/9 - 7x/9 = 7(1 - x)/9;
Thus, fraction of votes that must be against of total votes = 1/18 + 7x/9 = (1 + 14x)/18;
and, fraction of votes that must be in favor of total votes = 1/6 + 7(1 - x)/9 = (17 - 14x)/18;
Ratio of votes must be against to must be in favor = [(1 + 14x)/18] / [(17 - 14x)/18] = 2/1
=> x = 11/14
The correct answer:
A
Hope this helps!
-Jay
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