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

Question

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

ID: 700308
(DS05766)

chetan2u · Accepted Answer

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

GMATGuruNY · Answer

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.

E

PKN · Answer

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)

PKN · Answer

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 ?

chetan2u · Answer

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

colorblind · Answer

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

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

Arithmetic Ratio and proportion

The task in this question is to determine whether, on the basis of statements 1 and 2, it is possible to calculate the number of members of the legislature who voted against a certain measure.

1. This statement, that 1/4 of the members of the legislature did not vote on the measure, is compatible with any number of members of the legislature voting against the measure. After all, any number among the 3/4 of the remaining members could have voted against the measure. Furthermore, based on statement 1, we do not know the number of members of the legislature (although we do know, based on this statement, that the number of members of the legislature is divisible by 4); NOT sufficient.

2. This statement describes a scenario, of 5 additional members of the legislature voting against the measure, and stipulates that 1/3 of the members of the legislature would have voted against the measure in the scenario. Given this condition, we know that the number of members of the legislature was divisible by 3, and that the legislature had at least 15 members (to allow for the “5 additional members of the legislature” that could have voted against the measure, for a total of 1/3 of the members voting against it). However, beyond this we know essentially nothing from statement 2. In particular, depending on the number of members of the legislature (which we have not been given), any number of members could have voted against the measure. For example, exactly one member could have voted against the measure, in which case the legislature would have had (1 + 5) × 3 = 18 members. Exactly two members could have voted against the measure, in which case the legislature would have had (2 + 5) × 3 = 21 members, and so on for 3 members voting against, 4 members voting against, etc.; NOT sufficient.

Considering the statements 1 and 2 together, the reasoning is similar to the reasoning for statement 2, but with the further condition that the total number of members of the legislature is divisible by 12 (so as to allow that both exactly 1/4 of the members did not vote on the measure while exactly 1/3 could have voted against the measure). For example, it could have been the case that the legislature had 24 members. In this case, 1/3 of the members would have been 8 members, and, consistent with statements 1 and 2, 3 of the members (8 − 5) could have voted against the measure. Or the legislature could have had 36 members, in which case, consistent with statements 1 and 2, (1/3)*(36) − 5 = 12 − 5 = 7 members could have voted against the measure.

Both statements together are still not sufficient.

Yes2GMAT · Answer

chetan2u

From 1)

1/4 (Vf+Va+Vd) = Va 
3 Va = Vf + Vd

From 2)

Va + 5 = 1/3 (Vf+Va+Vd)

2Va + 15= Vf+Vd

From 1 and 2

2Va+15=3Va

Which we can solve to find Va.

What am i doing wrong here?

Thanks a lot for the solution you posted.

Bunuel · Answer

The first thing I'd say is that you are using too many variables, which could, and as it turns out did, confuse you. You really should plug in numbers for this question, or at least use fewer variables.

Next, from (1) we'd have 1/4(f + a + d) = d NOT 1/4(f + a + d) = a. Thus, for (1) + (2) we'd have f = 3d - a and f = 2a - d + 15, which cannot be solved for a.

Yes2GMAT · Answer

Bunuel

Thanks a lot Bunuel. Yes, transferring the variables onto the page while trying to read the question can be difficult at times. Wording for some of the questions isn't the best or quite easy to overlook. Hope i wont face the same issue on my my next GMAT attempt.

exdolore · Answer

Assuming the following variables: 
A = against
F = for
N = neutral
T = Total

Then we have these equations:
1/4 = N/T
3/4 = (A + F)/T (since one-fourth didn't vote, we know that three-fourth voted, either for or against)
(A+5)/T = 1/3
A = T - N - F

With these four equations, shouldn't we be able to solve for A using A = T - N - F?

T can be derived as a function of A from (A+5)/T = 1/3
N as a function of A from 1/4 = N/T and (A+5)/T = 1/3
F as a function of A from 3/4 = (A + F)/T and (A+5)/T = 1/3

Why doesn't that work?  Bunuel

Bunuel · Answer

The short answer is: that fourth equation is not actually giving you new information. Look at your equations:

1/4 = N/T, so N = T/4 
 3/4 = (A + F)/T , so A + F = 3T/4 
 (A + 5)/T = 1/3 
 A = T - N - F

Now plug (1) and (2) into (4):

From (1): N = T/4
 From (2): A + F = 3T/4, so A = 3T/4 - F

Equation (4) says:
A = T - N - F
 = T - T/4 - F
 = 3T/4 - F

But that is exactly the same as A = 3T/4 - F from equation (2).

So equation (4) is just a rearrangement of (1) and (2). It is not independent. That means you do NOT have 4 independent equations for 4 unknowns. You only have 3 independent equations (N = T/4, A + F = 3T/4, (A + 5)/T = 1/3) and 4 unknowns, so you still have one degree of freedom. That is why you end up with multiple possible integer pairs (A, T) and cannot pin down a single value of A.

exdolore · Answer

wow dang.. What a fruitless rabbit hole that I went down!

Thanks for breaking that down,  Bunuel !

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

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