Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This problem tests our understanding of fractions. Any time we see a fraction on the GMAT there is a good chance that they will give us one part of the fraction but will ask us about the other part. For example, if we were told that 1/3 of the total people in a room were women we could say that 2/3 must be men. This can easily be checked by adding the two fractions together; if we get a sum of 1, then we have done this correctly. (Note that 1/3 + 2/3 = 1.)
The example above is quite similar to what we have in this problem. We are told 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 result in 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 again the resolution and still have it pass.
Answer: E
Here’s another way to think about the problem:
Notice that 2/3 x 40 = 80/3 = 26 2/3 and we have to round this up to 27 because we can’t have a fraction of a person. 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.
