Hi All,

In these types of questions, it's important to remember that you can't have a 'fraction of a person.' Thus, you have to pay attention to the question that is ASKED and think in terms of 'whole persons.'

Here, we're told that AT LEAST 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. Since 2/3 of 40 is 26.666666, but we can't have 26.666666 people, we have to round UP to 27. In contrast, 26 people would NOT be enough, since 26/40 = 13/20 = 65% (and not the 66 2/3% minimum that a resolution needs to be passed).

Knowing that it would take AT LEAST 27 people to pass a resolution, the GREATEST number who could vote AGAINST the resolution in this case would be 40-27 = 13.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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