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

Question

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

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

PS65402.01

Bunuel · Accepted Answer

If we use a variable for the total number of votes, there will be too many fractions to manipulate. So, let's choose a smart number: set the total number of votes at 18.

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

For the ratio of those who voted against to those who voted for to be 2 to 1, there should be a total of 18*2/3 = 12 people who voted against. Therefore, in the remaining 14 votes, there should be 12 - 1 = 11 people who voted against. Hence, 11/14 of the remaining votes must be against.

Answer: A.

dkumar50 · Answer

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

AbeinOhio · Answer

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

PareshGmat · Answer

Did in the same way, just created a table as below

Probus · Answer

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}

Probus

EMPOWERgmatRichC · Answer

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

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

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.

Answer: A

Nums99 · Answer

VeritasKarishma   Bunuel ,

Hi Experts, 
I am really confused with what the question says here. 
I.E. 2:1 ratio 'against the resolution'
Shouldn't this mean 2x for the resolution and 1x against the resolution

KarishmaB · Answer

"2:1 against" means "2 against and 1 for"

"2:1 for" means "2 for and 1 against"

The first term of the ratio gives the number corresponding to what is mentioned. 
If "against" is mentioned, then the 2 is "against".

Dip050701 · Answer

so that the total count will result in a vote of 2 to 1 against the resolution? what does this mean in mathematical language ?

EMPOWERgmatRichC · Answer

Hi Dip050701, If you are approaching this question algebraically - and you choose specific variables to refer to "for" and "against" (for example... "F" = the number of votes FOR the resolution and "A" = the number of votes AGAINST the resolution), then 2 to 1 against would be F/A = 2/1. Of course, you can approach this question in a number of different ways (which you'll see in the other posts in this thread). Since the arithmetic involved is fairly simple, I chose to TEST VALUES. Here's how: 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 GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com www.empowergmat.com

Yuki2202 · Answer

Thank you for your explanation. But could you help me understand why can we know the total number is 18 instead of other number.
Thank you so much.

Bunuel · Answer

The total number of votes is not necessarily 18. I chose 18 because it's the smallest number that allows both 2/9 of the votes and 2/9*3/4 of the votes to be an integers, which easies the calculations. However, the total number of voters can be any multiple of 18.

Yuki2202 · Answer

Bunuel  I understood. Thank you so much!!!

findingmyself · Answer

Hey Bunuel, Please check if this approach is correct:

I took a smart number of 36.

The questions want us to have a 2:1 Majority which means 24 votes against the resolution minimum and 12 votes in favor.

Counted votes=(2/9)*36=8
Favour: (3/4)*8=6
Non-Favour=2

We need 22 more votes against the resolution to hit 2:1
Number of votes yet to be counted=28
Let (a/b) be the fraction of the remaining votes against the resolution.
28*(a/b)=22
(a/b)=22/28=11/14

rak08 · Answer

I don't get it where am I going wrong,,  KarishmaB   ScottTargetTestPrep

(1/18+(1-X)7/9)
-------------------- = 2 / 1
3/18 + 7X/9

which is against to in favour.

x comes out to be 9/14 so (1-x) = 5/14 
so not counted fraction is 5/14

Please guide!

Bunuel · Answer

You're actually solving for the wrong variable. The question asks what fraction of the remaining votes must be against, which means your final answer should be 1 - x, not x.

Your equation gives x = 3/14, so 1 - x = 11/14, which is the correct answer.

To get the required fraction directly, you should have set up:

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

Even better approach would be to assume values, as done in the official solution.

GMATCoachBen · Answer

This is good, I also picked 36 for the total, based on the LCM of the denominators (2/9 and 3/4). We can use a tree diagram to be organized and efficient: https://gmatclub.com/forum/download/file.php?id=86130 GMAT-Club-Forum-l97pse0h.png

GMATCoachBen · Answer

Note that the word " remaining" is a common signal word — and an essential clue that we must subtract from the total. Here's another good one to try: https://gmatclub.com/forum/of-the-3-600 ... ml#p307338

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

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