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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 [#permalink] New post 05 Dec 2012, 07:05
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Question Stats:

71% (01:42) correct 29% (00:53) wrong based on 254 sessions
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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Re: At least 2/3 of the 40 members of a committee must vote in [#permalink] New post 05 Dec 2012, 07:10
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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] New post 28 Sep 2013, 23:12
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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] 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] 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] 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] 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
Re: At least 2/3 of the 40 members of a committee must vote in   [#permalink] 21 Feb 2014, 15:21
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