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

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When 2/9 of the votes on a certain resolution have been [#permalink] New post 02 Mar 2012, 09:44
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Question Stats:

64% (04:16) correct 36% (02:16) wrong based on 92 sessions
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
[Reveal] Spoiler: OA
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Re: PT #9 PS 8 Q 20 [#permalink] New post 02 Mar 2012, 09:55
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eybrj2 wrote:
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


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.
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Re: When 2/9 of the votes on a certain resolution have been [#permalink] New post 02 Mar 2012, 09:59
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Final Result needs to be 2/3 Not in Favor

We already know of the 2/9th counted that we have 2/9 * 1/4 = 1/18

So then the question is how much of the 7/9 to go do we need to get to 2/3

Or:

1/18 + (7* x)/9 = 2/3

(14y +1)/18 = 2/3
14y+1= 12
y = 11/14 or answer is A
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Re: When 2/9 of the votes on a certain resolution have been [#permalink] New post 02 Mar 2014, 07:02
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Re: PT #9 PS 8 Q 20 [#permalink] New post 02 Mar 2014, 19:09
Bunuel wrote:
eybrj2 wrote:
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


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.


Did in the same way, just created a table as below
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Re: PT #9 PS 8 Q 20 [#permalink] New post 17 Mar 2014, 19:30
Bunuel wrote:
eybrj2 wrote:
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


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.....Not understood ....Pleas clarify

Answer: A.


Hi Bunuel
My fault ...now i understood.....
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Re: When 2/9 of the votes on a certain resolution have been [#permalink] New post 04 May 2014, 23:39
eybrj2 wrote:
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


Let's say there were 90 votes.
2/9 Votes = 20
Out of 20 3/4 in favour = 15 and remaining against = 5

For 2:1 against to favour ratio out of 90 votes= 30:60
Mores votes needed against = 60 - 5 = 55
Remaining votes = 90-20 = 70

Ratio to remaining = 55:70 = 11:14
Re: When 2/9 of the votes on a certain resolution have been   [#permalink] 04 May 2014, 23:39
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