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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Dec 08, 2019 6:57 pm

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

OA A

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Sun Dec 08, 2019 6:57 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Sun Dec 08, 2019 9:05 pm

BTGmoderatorDC 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

OA A

Source: Official Guide

Fraction of votes in favor of the counted votes = 2/9 * 3/4 = 1/6;
Thus, fraction of votes against the counted votes = 2/9 - 1/6 = 1/18;

Remaining uncounted votes = 1 - 2/9 = 7/9;

Say x is the fraction of uncounted votes that must be against the resolution of the uncounted votes so that the total count will result in a vote of 2 to 1 against the resolution

Fraction of votes that must be against of the uncounted votes = 7/9*x = 7x/9;
Thus, fraction of votes that must be favor of the uncounted votes = 7/9 - 7x/9 = 7(1 - x)/9;

Thus, fraction of votes that must be against of total votes = 1/18 + 7x/9 = (1 + 14x)/18;
and, fraction of votes that must be in favor of total votes = 1/6 + 7(1 - x)/9 = (17 - 14x)/18;

Ratio of votes must be against to must be in favor = [(1 + 14x)/18] / [(17 - 14x)/18] = 2/1

=> x = 11/14

The correct answer: A

Hope this helps!

-Jay
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by [email protected] » Mon Dec 09, 2019 3:23 pm

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Dec 10, 2019 7:14 pm

BTGmoderatorDC 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

OA A

Source: Official Guide

If 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 to1 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 against (and 30 votes for) the resolution, so the fraction is 110/140 = 11/14.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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