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

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Princeton Review

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

OA B.
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by deloitte247 » Sun Nov 11, 2018 12:27 pm
Vote against the proposal = 40% of the Total votes
Vote for the proposal = 100 - 40 = 60% of the Total vote
Total vote is unknown
$$Let\ total\ vote\ =\ x$$
of the total vote x, 80 more were in favor of the proposal than were against it ; thus
$$\left(60\%\ of\ \ x\right)-\left(40\%\ of\ x\right)=80$$
$$\left(\frac{60}{100}\cdot x\right)-\left(\frac{40}{100}-x\right)=80$$
$$0.6x-0.4x=80$$
$$0.2x=80$$
dividing both sides by the coefficient of x
$$\frac{0.2x}{0.2}=\frac{80}{0.2}$$
$$x=400$$
$$answer\ is\ Option\ B$$
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by Scott@TargetTestPrep » Mon Jan 21, 2019 6:11 pm
AAPL wrote:Princeton Review

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
Let x = the total number of votes cast. So 0.4x votes were against the proposal, and 0.6x votes were in favor of the proposal. We can create the equation:

0.6x - 0.4x = 80

0.2x = 80

x = 400

Answer: B

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by [email protected] » Tue Jan 22, 2019 10:54 am
Hi All,

We're told that of the votes cast on a certain proposal, 80 MORE were in favor of the proposal than were against it and the number of votes against the proposal was 40 percent of the TOTAL vote. We're asked for the total number of votes cast? (Each vote cast was either in favor of the proposal or against it). This question can be approached in a number of different ways, including by TESTing THE ANSWERS.

To start, since the difference between the number of "yes" votes and the number of "no" votes is 'round number' (in this case, 80), it's likely that the TOTAL number of votes is ALSO a 'nice' round number. We have two of those in the answer choices (re: 400 and 300). Let's TEST Answer B first.

Answer B: 400 votes
IF... there are 400 votes,
then 40% of the 400 were "no" votes --> (.4)(400) = 160
and the remaining 400 - 160 = 240 were "yes" votes
The difference in "yes" votes and "no" votes is 240 - 160 = 80
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

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Rich
Contact Rich at [email protected]
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by fskilnik@GMATH » Wed Jan 23, 2019 4:02 am
AAPL wrote:Princeton Review

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

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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Sun Jan 27, 2019 6:13 pm
AAPL wrote:Princeton Review

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
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

Scott Woodbury-Stewart
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[email protected]

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