Of the votes cast on a certain proposal, 80 more were in favor of the

Question

Of the votes cast on a certain proposal, 80 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160

(A) 480
(B) 400
(C) 300
(D) 240
(E) 160

anudeep133 · Answer

Solution :  Let x be no. of votes against the proposal. Then no. of votes in favor would be x+80 and total no. of votes would be 2x+80.
40%(2X + 80) = X ==> X=160.
Total no. of votes = 2(160) + 80 = 400

Option B

Skywalker18 · Answer

Let the total number of votes cast = T
Number of votes cast in favour of proposal = F
Number of votes cast against the proposal = A

F = A + 80 -- 1
Since , the number of votes against the proposal was 40 percent of the total vote
A= (40/100)*T = .4T -- 2
=> F = (60/100)*T = .6T -- 3

From equations 1 , 2 and 3 ,we get
.2T = 80
=> T= 400
Answer B

whitehalo · Answer

Let   x   be the total of votes cast, the solution we want.
Number of people against the proposal:  \frac{40}{100}  x
Number of people in favor: 1 -  \frac{40}{100}  x =  \frac{60}{100}  x

Since, 
that means 80 is the difference of the two percentages. 
 \frac{60}{100}  x -  \frac{40}{100}  x =  \frac{20}{100}  x

\frac{20}{100}  x = 80
x = 400

CounterSniper · Answer

favour of proposal =x+80
against the proposal=x
total votes =2x+80
now,
.4(2x+80)=x
.8x+32=x
.2x=320
x=320/2=160=votes against
total votes =320+80=400

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing THE ANSWERS.

Under normal circumstances, we would start by TESTing Answer B or D first. Since B is the 'easier' value, we'll start there...

Answer B: 400 total votes

We're told that 40% of the total votes were votes AGAINST the proposal:
(.4)(400) = 160 votes against

So the remaining votes were in FAVOR of the proposal:
400 - 160 = 240 votes for

With these two numbers, the difference is 240-160 = 80, which is a MATCH for what we were told. Thus, this MUST be the answer.

Final Answer:  B

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

Temurkhon · Answer

Against = x
For = x+80

get proportion

x/x+x+80=4/10

10x=8x+320 => x=160, so total number = 160*2+80=400

B

chetan2u · Answer

Hi,
 Although a relatively simpler Question, fast thinking can save time for slightly complex Qs later.. 
IF votes against are 40 %, votes for will be 60%.
the difference is 20% which is given as 80..
so total will be 80/20 * 100=400
B

fskilnik · Answer

? = t\left( {{\rm{total}}} \right)\,\,\,\,\left\{ \matrix{
 \,{\rm{against}}\,\,\,{\rm{ = }}\,\,a\,\,\mathop = \limits^{{\rm{stem}}} \,\,{2 \over 5}t \hfill \cr 
 \,{\rm{for}}\,\,{\rm{ = }}\,\,t - a\,\,\mathop = \limits^{{\rm{stem}}} \,\,80 + a\,\,\, \Rightarrow 2a = t - 80 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,2\left( {{2 \over 5}t} \right) = t - 80\,\,\,\, \Rightarrow \,\,\,{1 \over 5}t = 80\,\,\,\, \Rightarrow \,\,\,\left( {\rm{B}} \right)

We follow the notations and rationale taught in the  GMATH  method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

We can let n = the total number of votes. Thus, 0.4n votes were against the proposal, and 0.6n votes were in favor of the proposal. We can create the equation:

0.6n - 0.4n = 80

0.2n = 80

n = 80/0.2 = 800/2 = 400

Answer: B

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Of the votes cast on a certain proposal, 80 more were in favor of the

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