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

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Jamesk486
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When 2/9 of the votes on a certain resolution have been coun [#permalink] New post   15 May 2007, 19:50
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65% (hard)

Question Stats:

62% (02:21) correct 38% (03:08) wrong based on 71 sessions
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When 2/9 of the votes on a certain resolution have been counted, 3/4 of thoes 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-2-9-of-the-votes-on-a-certain-resolution-have-been-128471.html

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A
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apache
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Re: When 2/9 of the votes on a certain resolution have been coun [#permalink] New post   15 May 2007, 20:05
total vote x.

2/9*1/4*x+7/9*a*x=2/3*x

now a= 11/14
so will pick A
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Re: When 2/9 of the votes on a certain resolution have been coun [#permalink] New post   15 May 2007, 22:19
Will go with (A).
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Re: When 2/9 of the votes on a certain resolution have been coun [#permalink] New post   15 May 2007, 22:27
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A

solved by picking numbers

Let total votes be 36 (LCM of 9 and 4 for easy calc)

so 2/9 = 8 votes => 6 for / 2 against

remaining votes = 36-8 = 28

now total 'for' req = 12 and total 'against' = 24 for 2:1

Since 2 votes are already against, 22 more votes shoulb be against the resolution => 22 out of remaining 28

= 22/28 = 11/14 = A :)
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Re: When 2/9 of the votes on a certain resolution have been coun [#permalink] New post   01 Mar 2014, 07:24
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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

If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.

"2/9 of the votes on a certain resolution have been counted" --> 4 counted and 18-4=14 votes left to be counted;
"3/4 of those counted are in favor of the resolution" --> 3 in favor and 1 against;

Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus 11/14 of the remaining votes must be against.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-2-9-of-the-votes-on-a-certain-resolution-have-been-128471.html

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Re: When 2/9 of the votes on a certain resolution have been coun [#permalink]
01 Mar 2014, 07:24
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