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# When 2/9 of the votes on a certain resolution have been

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Director
Joined: 14 Sep 2005
Posts: 985
Location: South Korea
When 2/9 of the votes on a certain resolution have been [#permalink]

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19 Nov 2005, 08:07
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When 2/9 of the votes on a certain resolution have
been counted, 3/4 of those counted are in favor of
the resolution. What fraction of the remaining votes
must be against the resolution so that the total
count will result in a vote of 2 to 1 against the
resolution?

(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14
_________________

Auge um Auge, Zahn um Zahn !

SVP
Joined: 24 Sep 2005
Posts: 1885

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19 Nov 2005, 08:24
gamjatang wrote:
When 2/9 of the votes on a certain resolution have
been counted, 3/4 of those counted are in favor of
the resolution. What fraction of the remaining votes
must be against the resolution so that the total
count will result in a vote of 2 to 1 against the
resolution
?

(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14

okie, i understand the bold part as : against/ for = 2/1 ...if misunderstanding from this point, go wrong for all
we have 3/4 of 2/9 X(= 1/6 X) ( X is the number of voters in all) as the number of voter favor of the resolution
we have Y*7/9X as the no of voter against blah blah ( Y is the asked fraction)
since against/ for = 2/1, we have : Y*7/9X= 2*1/6 X ---> Y= 3/7
SVP
Joined: 24 Sep 2005
Posts: 1885

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19 Nov 2005, 08:48
gamjatang wrote:
When 2/9 of the votes on a certain resolution have
been counted, 3/4 of those counted are in favor of
the resolution. What fraction of the remaining votes
must be against the resolution so that the total
count
will result in a vote of 2 to 1 against the
resolution?

(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14

sorrie, looks like i misread one point, the bold part.
the no of voters against in all : Y*7/9X + 1/18 X = A
the ...................for..............: (1-Y)* 7/9 X+ 1/6 X= B

since A:B= 2:1 , we have
Y*7/9X+1/18X= 2*(1-Y)*7/9X + 2*1/6 X
---> 7/9Y+1/18= 14/9 - y*14/9 +1/3
---> 21/9Y= 14/9+1/3- 1/18 = 11/6 --> Y= 11/6 / 21/9 = 11/14

Btw, I think we can partially employ the lucky twins shortcut provided by Matt earlier
Manager
Joined: 11 Jul 2005
Posts: 86
Location: New York

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19 Nov 2005, 16:25
gamjatang wrote:
When 2/9 of the votes on a certain resolution have
been counted, 3/4 of those counted are in favor of
the resolution. What fraction of the remaining votes
must be against the resolution so that the total
count will result in a vote of 2 to 1 against the
resolution?

(A) 11/14
(B) 13/18
(C) 4/7
(D) 3/7
(E) 3/14

Let the total no: of votes be 36 (since the fractions have 9 and 4, I assumed 36 would be a favourable number)

2/9*36= 8 votes are counted and 28 remains uncounted
3/4*8=6 in favour and 2 against.
1/2=(6+28(1-x))/2+28x

x= 11/14 (A)
VP
Joined: 06 Jun 2004
Posts: 1053
Location: CA

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19 Nov 2005, 19:30
Yup, got A as well. Picking numbers seems to be the easiest for this type of questions.
19 Nov 2005, 19:30
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