Problem Solving

uptowngirl92 wrote:Atleast 2/3 of the 40 members of a committee must vote in favour of a resolution for it to pass.What is the greatest number of members who could vote against the resolution and still have it pass?
A. 19
B. 17
C. 16
D. 14
E. 13

I keep on getting this ques. wrong i don't know why.Here's my solution:
2/3 x 40=2 x 13.333.. = 2 x 13 =26
Therefore, 26 are in favour and 14 are against.Ans:14.WRONG.

However if we approach the other way around and start by calculating members against the resolution,
1/3 x 40=13.333..=13.Ans: 13 which is the correct ans.

Can somebody please point out the flaw?

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.

The answer is 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.