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# How many members of a certain legislature voted against the measure to

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Math Expert
Joined: 02 Sep 2009
Posts: 59147
How many members of a certain legislature voted against the measure to  [#permalink]

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03 Aug 2018, 00:00
22
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Difficulty:

25% (medium)

Question Stats:

73% (01:39) correct 27% (01:30) wrong based on 546 sessions

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How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

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Posts: 8195
Re: How many members of a certain legislature voted against the measure to  [#permalink]

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05 Aug 2018, 23:14
9
1
PKN wrote:
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

Hi chetan2u,
Could you please explain this question?
Thanking you.

types of people..
1) Did not vote......d
2) voted for..........f
3) voted against...a

we are looking for $$\frac{a}{(d+f+a)}$$

(1) 1/4 of the members of the legislature did not vote on the measure.
so$$d=\frac{t}{4}=\frac{(d+f+a)}{4}........4d=d+f+a......f+a=3d$$
nothing much
insuff

(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
now a becomes a+5
so $$\frac{a+5}{d+f+a}=\frac{1}{3}........3a+15=d+f+a.......2a+15=d+f$$
insuff

combined
three variables, two equation.. ans not possible
insuff

E
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How many members of a certain legislature voted against the measure to  [#permalink]

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03 Aug 2018, 03:34
1
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

We have two options here ON & OFF.

Employees can VOTE ON or VOTE AGAINST. Total #employees=voted ON+Voted AGAINST

Question stem:- # employees VOTE AGAINST=?

St1:- 1/4 of the members of the legislature did not vote on the measure.
Total # of employees is not provided. We can't determine # employees VOTE AGAINST.
Insufficient.

St2:-If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
Here, neither #employees voted ON nor total #of employees is provided.
So, insufficient.

Combining, let total#of employees be x.
from st(1), we have , #of employees voted AGAINST=$$\frac{x}{4}$$
From st(2), we have, $$\frac{\frac{x+5}{4}+5}{x+5}$$=$$\frac{1}{3}$$
We can determine x, hence $$\frac{x+5}{4}$$ can be determined.
Note:- $$\frac{x+5}{4}$$ is the # employees VOTE AGAINST.
No need of exact computation.

Ans. (C)
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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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03 Aug 2018, 15:51
PKN wrote:
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

We have two options here ON & OFF.

Employees can VOTE ON or VOTE AGAINST. Total #employees=voted ON+Voted AGAINST

Question stem:- # employees VOTE AGAINST=?

St1:- 1/4 of the members of the legislature did not vote on the measure.
Total # of employees is not provided. We can't determine # employees VOTE AGAINST.
Insufficient.

St2:-If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
Here, neither #employees voted ON nor total #of employees is provided.
So, insufficient.

Combining, let total#of employees be x.
from st(1), we have , #of employees voted AGAINST=$$\frac{x}{4}$$
From st(2), we have, $$\frac{\frac{x+5}{4}+5}{x+5}$$=$$\frac{1}{3}$$
We can determine x, hence $$\frac{x+5}{4}$$ can be determined.
Note:- $$\frac{x+5}{4}$$ is the # employees VOTE AGAINST.
No need of exact computation.

Ans. (C)

Hi,

Take care that Statement 1 talks about No voting. It was not about voters against the measure.
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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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03 Aug 2018, 16:28
never seen a question type like this. are they common in the math section? guess i'm lucky though since I got this one wrong, actually
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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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05 Aug 2018, 22:59
PKN wrote:
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

We have two options here ON & OFF.

Employees can VOTE ON or VOTE AGAINST. Total #employees=voted ON+Voted AGAINST

Question stem:- # employees VOTE AGAINST=?

St1:- 1/4 of the members of the legislature did not vote on the measure.
Total # of employees is not provided. We can't determine # employees VOTE AGAINST.
Insufficient.

St2:-If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
Here, neither #employees voted ON nor total #of employees is provided.
So, insufficient.

Combining, let total#of employees be x.
from st(1), we have , #of employees voted AGAINST=$$\frac{x}{4}$$
From st(2), we have, $$\frac{\frac{x+5}{4}+5}{x+5}$$=$$\frac{1}{3}$$
We can determine x, hence $$\frac{x+5}{4}$$ can be determined.
Note:- $$\frac{x+5}{4}$$ is the # employees VOTE AGAINST.
No need of exact computation.

Ans. (C)

Hi chetan2u,
Could you please explain this question?
Thanking you.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 995
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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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05 Aug 2018, 23:21
1
chetan2u wrote:
PKN wrote:
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

Hi chetan2u,
Could you please explain this question?
Thanking you.

types of people..
1) Did not vote......d
2) voted for..........f
3) voted against...a

we are looking for $$\frac{a}{(d+f+a)}$$

(1) 1/4 of the members of the legislature did not vote on the measure.
so$$d=\frac{t}{4}=\frac{(d+f+a)}{4}........4d=d+f+a......f+a=3d$$
nothing much
insuff

(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
now a becomes a+5
so $$\frac{a+5}{d+f+a}=\frac{1}{3}........3a+15=d+f+a.......2a+15=d+f$$
insuff

combined
three variables, two equation.. ans not possible
insuff

E

In statement 2, when 5 additional members were added to 'a', Doesn't the total member become a+5+d+f ?
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Math Expert
Joined: 02 Aug 2009
Posts: 8195
Re: How many members of a certain legislature voted against the measure to  [#permalink]

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05 Aug 2018, 23:37
1
PKN wrote:
chetan2u wrote:
PKN wrote:

Hi chetan2u,
Could you please explain this question?
Thanking you.

types of people..
1) Did not vote......d
2) voted for..........f
3) voted against...a

we are looking for $$\frac{a}{(d+f+a)}$$

(1) 1/4 of the members of the legislature did not vote on the measure.
so$$d=\frac{t}{4}=\frac{(d+f+a)}{4}........4d=d+f+a......f+a=3d$$
nothing much
insuff

(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3
now a becomes a+5
so $$\frac{a+5}{d+f+a}=\frac{1}{3}........3a+15=d+f+a.......2a+15=d+f$$
insuff

combined
three variables, two equation.. ans not possible
insuff

E

In statement 2, when 5 additional members were added to 'a', Doesn't the total member become a+5+d+f ?

No,

5 is already part of total, they could be initially part of NOT voted or voted for
total will remain the same..
5 additional members of the legislature.. so they are part of total, just shifting sides
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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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06 Aug 2018, 00:19
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

NEW question from GMAT® Quantitative Review 2019

(DS05766)

Dear GMATGuruNY

Can you please weigh in with best to solve this question?
Thanks
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How many members of a certain legislature voted against the measure to  [#permalink]

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06 Aug 2018, 02:27
1
Bunuel wrote:
How many members of a certain legislature voted against the measure to raise their salaries?

(1) 1/4 of the members of the legislature did not vote on the measure.
(2) If 5 additional members of the legislature had voted against the measure, then the fraction of members of the legislature voting against the measure would have been 1/3

Statements combined:

Case 1: Total members = 24
Non-voters = $$\frac{1}{4} * 24 = 6$$
Since $$\frac{1}{3} * 24 = 8$$, 5 additional members would bring the number who voted against the measure to 8, implying that 3 members actually voted against the measure.

Case 2: Total members = 48
Non-voters = $$\frac{1}{4} * 48 = 12$$
Since $$\frac{1}{3} * 48 = 16$$, 5 additional members would bring the number who voted against the measure to 16, implying that 11 members actually voted against the measure.

Since the number who voted against can be different values, the two statements combined are INSUFFICIENT.

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Re: How many members of a certain legislature voted against the measure to  [#permalink]

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24 Feb 2019, 17:54
x = voted for
y = voted against
z = did not vote
T = total = x+y+z
St1 & St2:
$$\frac{z}{T} = \frac{1}{4}$$
$$\frac{(y+5)}{T} = \frac{1}{3}$$ OR $$\frac{(y+5)}{T} = \frac{(1*n)}{(3*n)}$$
y+5 = n
y+5 = 1,2,3...…..
Not Suff
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Re: How many members of a certain legislature voted against the measure to   [#permalink] 24 Feb 2019, 17:54
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