tj123 wrote:At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resoltion and still have it pass?
A) 19
B) 17
c) 16
D) 14
e) 13
We are given that at least 2/3 of the members must vote IN FAVOR of a resolution in order for it to pass; however, we need to determine the greatest number of members who could vote AGAINST the resolution and still cause its passage. Remember, in a vote there are only two options, voting in FAVOR and voting AGAINST. Thus, we know the following:
2/3 of total voters need to vote in FAVOR for it to pass; this means that 1/3 of total voters can vote AGAINST for it to pass.
To finish the problem, we can set up the following equation:
1/3 x 40 = total votes AGAINST to have resolution pass
1/3 x 40 = 40/3 = 13 1/3 voters
Since we need the resolution TO PASS, we must round this number down to 13. Thus, 13 voters can vote against the resolution and still have it pass.
Alternate Solution:
Notice that 2/3 x 40 = 80/3 = 26 2/3 and we have to round this up to 27 because 26 people out of 40 does not satisfy the requirement of "at least 2/3 of the voters". . Therefore, we need at least 27 voters to vote IN FAVOR of the resolution to pass it. This means that we can have at most 40 - 27 = 13 individuals voting AGAINST it, and still it will pass. Therefore, the maximum number of voters who can vote against it and still have it pass is 13.
Answer:
E.gif)
