At least 2/3 of the 40 members of a committee must vote in

Since, at least 2/3 of the 40 members of a committee must vote in favor, then at least \(\frac{2}{3}*40=26\frac{2}{3}\) or at least 27 members should vote in favor. Therefore at most 13 members could vote against.

Answer: E.
_________________

What is wrong in the way I am doing this question?

It is given that at least 2/3rd of the 40 members should vote for the resolution. Since the members have to be a positive integer, I have considered 40 as 39 and then divided it by 3. After calculation, 26 members should vote for resolution. The remaining are 14 members who can vote against it; I marked D, which is incorrect.

Well you calculated for 39 members...How about the 1 that you left out....Since the Questions says At least 2/3 of 40 which is 26.666....Now atleast means it can be more and the least possible Integer value is 27....So most 13 members can vote against.
_________________

40/3 = 13.3 (approx).. --> 13.3 x 2 = 26.6, so at least 27 people have to vote in favor for it to pass. ----> 13 at most can vote against for it to pass.

Dividing 40/3 gives us 13.33333, thus 2/3 = 26.6666.. So in order for it to pass, at least 26.6 people need to vote on it, but of course we need an integer so at least 27 people need to vote on it (so, in practice, a bigger portion than 2/3).. That leaves us with 13 people that can vote against and still have it pass.

The non-integer throws us off and in some cases makes us round down. I think that's what they primarily want to test us on in this case, if we understand that we should round UP for required votes instead of round down.

The way I calculated was. At least 2/3 so it's the minimum than the greatest portion we would have left would be 1/3. Hence (40x1)/3 13,3... = 13 people

2/3 of 40 which is 26.666, there is no 0.666 person, so I decided 2/3 of 40 is 26, thus 40-26=14, at least means minimum, not maximum, so minimum possible numbers, then it's logical to consider 26, moreover question asks the greatest number of members, how could I realize wherther to round up or not?

Thanks!

Hi studentsensual,

You seem to understand that you can't have a 'fraction of a person' in these types of questions. 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:

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

So, when dealing with individuals, should I every time to round the numbers up?
Thanks!

Hi studentsensual,

If a question expects you to 'round up' or 'round down', then you have to make sure to choose the answer that focuses on the specifics of the given prompt and answers the question that is asked:

Here, the specific information stated that AT LEAST 2/3 (meaning at least 66 2/3%) of the members must vote in favor of a resolution for it to pass. Since 26/40 is only 65%, then 26 people would NOT be enough. Thus, you have to round that number UP to 27 (because that's what the question requires). There could conceivably be questions that would require you to round down, but that's not what THIS question required.

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

Please compare these questions:

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 resolution and still have it pass?
(A) 19
(8) 17
(C) 16
(D) 14
(E) 13

A club collected exactly $599 from its members. If each member contributed at least $12, what is the greatest number of members the club could have?
(A) 43
(B) 44
(C) 49
(D) 50
(E) 51

599/12=49.912
Since n represents individual people, it must be a whole number; the greatest possible value of n is thus 49, not 50

Hi studentsensual,

These two questions provide you with different types of information/situations, so they require that you round in different 'directions.' In the second prompt, we're told that each member contributed AT LEAST $12, but that the total collected was $599. In this situation, the total number of members CANNOT be 50, since 50($12) = $600 - and that total is just a little TOO HIGH. As such, we have to round DOWN.

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

Atleast 2/3 votes in favor mean 2/3 of 40 ~27. Hence, Max against would be 40-27 = 13. hence E
_________________

Vote in favour -

\(\frac{2}{3} * 40\) = \(26 \frac{2}{3}\) ~ 27

No of voters who can vote against the resolution and still get it passed is (40 - 27) 13

Hence answer will be (E)
_________________

Hi Manonamission,

One of they 'keys' to this question is 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:

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

At least \(\frac{2}{3}\) of 40 people must vote for a resolution to pass.

\(\frac{2}{3}\) * 40 = 26\(\frac{2}{3}\), or 26.67 persons

In this problem, if you are torn between rounding up to 27 or down to 26, one way to check is mentioned briefly by EMPOWERgmatRichC above: reverse the process, though I will include both numbers in question. Divide both numbers by 40.

\(\frac{26}{40}\) = .65, or 65%

\(\frac{27}{40}\) = .675, or 67.5%

26 is not enough: 65 percent is not "at least" 66.67 percent. It doesn't matter that 27 is a bit too much.

You cannot have a fraction of a person, and 27 clears the hurdle of at least 66.67%, while 26 does not.

If 27 must vote "yes," only 40 - 27 = 13 can vote "no."

Answer E
_________________

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 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.

Answer: E
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________