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# When 2/9 of the votes on a certain resolution have been counted, 3/4

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When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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02 Mar 2012, 09:44
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63% (02:45) correct 37% (03:13) wrong based on 592 sessions

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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

PS65402.01
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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#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 counted, 3/4  [#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 counted, 3/4  [#permalink]

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02 Mar 2014, 19:09
4
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: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#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 counted, 3/4  [#permalink]

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04 May 2014, 23:39
3
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 counted, 3/4  [#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 counted, 3/4  [#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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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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14 Nov 2015, 10:23
1
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 counted, 3/4  [#permalink]

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06 Mar 2019, 10:01
1
Hi here are my two cents for this questions

Well there can be multiple ways to solve this questions depends on which method strikes you at that moment.

However, its noteworthy to see what can we derive from the information given

We are told that ratio of $$\frac{NF}{F}= \frac{2}{1}$$

this mean$$\frac{2}{3}=\frac{NF}{NF+F}$$ and $$\frac{1}{3}=\frac{F}{NF+F}$$

we are told that $$\frac{2}{9}$$ of votes are counted and of which $$\frac{3}{4}$$ are in favor of proposal. that means $$\frac{1}{4}$$ are against the proposal.

what remains to be counted is $$\frac{7}{9}$$.then let the fraction of votes against the proposal be 'a' , then number of votes for the resolution will be (1-a) and total number of votes =x

then
$$\frac{2x}{3}$$ = $$\frac{2x}{9}$$ $$\frac{1}{4}$$ + $$\frac{7x}{9}$$ a

Simplyfying the above equation we have
a= $$\frac{11}{14}$$

Alternatively if one is good at algebriac approach then

$$\frac{NF}{F}$$=$$\frac{\frac{2x}{9}\frac{1}{4} +\frac{7x}{9} a }{\frac{2x}{9}\frac{3}{4} +\frac{7x}{9}(1- a )}$$

$$\frac{2}{1}$$=$$\frac{\frac{2x}{9}\frac{1}{4} +\frac{7x}{9} a }{\frac{2x}{9}\frac{3}{4} +\frac{7x}{9}(1- a )}$$

solving we get a= $$\frac{11}{14}$$

Alternatively,
we see that if there were 36 votes (how did we come at 36 , we take the LCM of denominators of $$\frac{2}{9} and \frac{3}{4}$$ )
then 8 are counted and 6 are in favor and 2 are against

remaining 28 votes x are in favor and y are against.then we have
$$\frac{2}{3}$$= y+2
solving we get y= 22

so we need $$\frac{y}{28}= \frac{22}{28}= \frac{11}{14}$$

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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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19 Oct 2019, 11:57
how do you get 2/3 of votes is needed for 2 to 1 ratio?
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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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31 Oct 2019, 10:47
1
Assume a total of 144 votes ( multiple of 4*9 as we have these in denominators of fractions)

Counted so far= 2/9*144 =32
Of these in favour =3/4*32=24
Against =9

Remaining= 144-32=112

Against: For must be 2:1 or 96:48

currently, we have 8:24

The fraction of remaining votes that must be against = 88/112 =44/56=22/28=11/14

Hence A
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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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09 Dec 2019, 16:54
Hi All,

We're told that when 2/9 of the votes on a certain resolution have been counted, 3/4 of those counted are in FAVOR of the resolution. We're asked 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. While this question might appear a little 'complicated', it's based on some basic Arithmetic and can be solved by TESTing VALUES.

Since we're dealing with 'ninths' and 'fourths', let's TEST a common denominator: 36

For the final ratio to be 2:1 AGAINST the resolution, we need there to be 24 votes AGAINST and 12 votes in FAVOR

IF.... there are 36 total votes
(2/9)(36) = 8 votes have been counted
(3/4)(8) = 6 of those 8 votes are in FAVOR of the resolution.... and the other 2 votes are AGAINST

36 - 8 = 28 votes remain
Since we already have 2 votes in AGAINST - and we need 24 total votes AGAINST, we need 22 of these remaining 28 votes to be AGAINST (and then the rest will be in FAVOR).
22/28 = 11/14

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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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12 Dec 2019, 18:46
1
eybrj2 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

PS65402.01

If we assume that there are 180 votes, then 2/9 x 180 = 40 votes have been counted. Of these 40 votes, 3/4 x 40 = 30 are in favor of the resolution and 10 are against the resolution. If the vote is 2 to 1 against the resolution, we can create the equation:

x + 2x = 180

3x = 180

x = 60

Therefore, we need to have 60 votes for the resolution and 120 votes against the resolution.

Since 10 votes are currently against the resolution, of the 140 remaining votes, we need 110 votes of them to be against (and 30 votes for) the resolution, so the fraction is 110/140 = 11/14.

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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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18 Dec 2019, 23:02
eybrj2 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

PS65402.01

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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4  [#permalink]

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14 Mar 2020, 13:19
Picking an number for number of votes helped to find solution quicker. I picked the number 18 [Based on bunuel's solution] and derived to answer quickly.

4 counted
3 Favor
1 Against

We have currently 1 against , so we need 11 more out of 14

Ans 11/14 - Option A
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Re: When 2/9 of the votes on a certain resolution have been counted, 3/4   [#permalink] 14 Mar 2020, 13:19