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

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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
[Reveal] Spoiler: OA
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Walkabout 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 resolution and still have it pass?

(A) 19
(8) 17
(C) 16
(D) 14
(E) 13


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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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AasaanHai wrote:
Bunuel wrote:
Walkabout 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 resolution and still have it pass?

(A) 19
(8) 17
(C) 16
(D) 14
(E) 13


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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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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:
[Reveal] Spoiler:
E


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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 28 Sep 2013, 22:32
Bunuel wrote:
Walkabout 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 resolution and still have it pass?

(A) 19
(8) 17
(C) 16
(D) 14
(E) 13


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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 19 Dec 2013, 01:38
Walkabout 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 resolution and still have it pass?

(A) 19
(8) 17
(C) 16
(D) 14
(E) 13



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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 10 Jan 2014, 00:39
Walkabout 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 resolution and still have it pass?

(A) 19
(8) 17
(C) 16
(D) 14
(E) 13



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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 21 Feb 2014, 15:21
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
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 26 Jan 2016, 21:59
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!

WoundedTiger wrote:
AasaanHai wrote:
Bunuel wrote:
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.
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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 31 Jan 2016, 18:31
So, when dealing with individuals, should I every time to round the numbers up?
Thanks!

EMPOWERgmatRichC wrote:
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:
[Reveal] Spoiler:
E


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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 31 Jan 2016, 22:50
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.

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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 04 Feb 2016, 05:00
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


EMPOWERgmatRichC wrote:
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.

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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 04 Feb 2016, 11:11
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.

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At least 2/3rd ofthe 40 members of a committee.. [#permalink]

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New post 04 Sep 2016, 07:53
At least 2/3rd ofthe 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
(B) 17
(C) 16
(D) 14
(E) 13
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Re: At least 2/3rd ofthe 40 members of a committee.. [#permalink]

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New post 04 Sep 2016, 09:18
Manonamission wrote:
At least 2/3rd ofthe 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
(B) 17
(C) 16
(D) 14
(E) 13


Atleast 2/3 votes in favor mean 2/3 of 40 ~27. Hence, Max against would be 40-27 = 13. hence E
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Re: At least 2/3rd ofthe 40 members of a committee.. [#permalink]

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New post 04 Sep 2016, 12:09
Manonamission wrote:
At least 2/3rd 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
(B) 17
(C) 16
(D) 14
(E) 13


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)

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Re: At least 2/3rd ofthe 40 members of a committee.. [#permalink]

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New post 04 Sep 2016, 19:59
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:
[Reveal] Spoiler:
E


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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink]

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New post 04 Sep 2016, 21:33
Manonamission wrote:
At least 2/3rd ofthe 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
(B) 17
(C) 16
(D) 14
(E) 13


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Re: At least 2/3 of the 40 members of a committee must vote in   [#permalink] 04 Sep 2016, 21:33
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