eybrj2 wrote:

When 2/9 of the votes on a certain resolution have been counted, 3/4 of thoes 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

Solution:

Lets use the plug in method to solve this question.

The question states that 2/9th of the votes are counted 3/4th are in favour of the resolution. Lets take a value for the the total number of votes. While we can take any value its smart to take a value which is a multiple of 9 as we know that the first part of the question says 2/9th of the votes are counted. Lets assume the total number of votes = 18.

Part 1 : 2/9 of the votes are counted = 2/9*18 = 4. It further states that 3/4 of the counted votes are in favour, which means 3/4*4 = 3 are in favour.

The question is asking what number of the remaining votes should be against the resolution such that we get a final count of 2:1 against the resolution.

Part 2: Which means: we need 2/3*18 = 12 votes against the resolution. We know from part 1 that 1 vote is against the resolution out of a total of 4 counted votes. Therefore we need another 11 votes out of a remaining (18-4) votes to be against the resolution to get a final ratio of 2:1.

Therefore the ratio of votes which need to be against the reolution out of the remaining votes will be = 11/14.

Thus, Answer is A.

Tip - It makes more sense to plug in a value for total number of votes rather than solving it in fraction form as it simplifies calculations.