When 2/9 of the votes on a certain resolution have been : GMAT Problem Solving (PS)
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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]

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02 Mar 2012, 09:44
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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
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Re: PT #9 PS 8 Q 20 [#permalink]

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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.

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Re: When 2/9 of the votes on a certain resolution have been [#permalink]

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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]

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02 Mar 2014, 07:02
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Re: PT #9 PS 8 Q 20 [#permalink]

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02 Mar 2014, 19:09
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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.

Did in the same way, just created a table as below
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Re: PT #9 PS 8 Q 20 [#permalink]

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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

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]

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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.
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
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Re: When 2/9 of the votes on a certain resolution have been [#permalink]

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09 Nov 2015, 07:07
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Re: When 2/9 of the votes on a certain resolution have been [#permalink]

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14 Nov 2015, 02:21
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

Solution:

Lets use the plug in method to solve this question.

The question states that 2/9th of the votes are counted 3/4th are in favour of the resolution. Lets take a value for the the total number of votes. While we can take any value its smart to take a value which is a multiple of 9 as we know that the first part of the question says 2/9th of the votes are counted. Lets assume the total number of votes = 18.

Part 1 : 2/9 of the votes are counted = 2/9*18 = 4. It further states that 3/4 of the counted votes are in favour, which means 3/4*4 = 3 are in favour.

The question is asking what number of the remaining votes should be against the resolution such that we get a final count of 2:1 against the resolution.

Part 2: Which means: we need 2/3*18 = 12 votes against the resolution. We know from part 1 that 1 vote is against the resolution out of a total of 4 counted votes. Therefore we need another 11 votes out of a remaining (18-4) votes to be against the resolution to get a final ratio of 2:1.

Therefore the ratio of votes which need to be against the reolution out of the remaining votes will be = 11/14.

Tip - It makes more sense to plug in a value for total number of votes rather than solving it in fraction form as it simplifies calculations.
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Re: When 2/9 of the votes on a certain resolution have been [#permalink]

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14 Nov 2015, 03:19
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

Based on the denominators in the fractions 2/9 and 3/4, let us assume there are 36 votes.

2/9 are counted i.e., 8 counted out of 36
3/4 of counted in favor i.e, 6 are in favor and 2 are against out of 8 counted
Against given 2 to 1 i.e, 24 to 12 against out of 36
Remaining against = 24-2=22
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When 2/9 of the votes on a certain resolution have been [#permalink]

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14 Nov 2015, 10:23
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?

Let the total number of voters be 36 ( LCM of the denominators 4 & 9)

eybrj2 wrote:
When 2/9 of the votes on a certain resolution have been counted

Total number of votes counted is (2/9*36) = 8
Total number of votes not counted is ( 36-8) = 28

eybrj2 wrote:
3/4 of thoes counted are in favor of the resolution.

Total number of voters in favour of the resolution whose votes have been counted is (8*3/4) =6
Total number of voters against whose votes have been counted is (8-6) = 2

eybrj2 wrote:
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?

Total number of votes required for 2 : 1 against the vote is = 36*2/3 =>24

Out of 24 total votes we already have 2 votes against the resolution so out of the remainin 28 votes ( which have not been counted) we required 24 votes.

So, The effective percentage of votes required is 22/28 =>11/14

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Re: When 2/9 of the votes on a certain resolution have been [#permalink]

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23 Nov 2016, 05:29
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Re: When 2/9 of the votes on a certain resolution have been   [#permalink] 23 Nov 2016, 05:29
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