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In a town, 80% of the men are registered voters

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sameer93
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In a town, 80% of the men are registered voters [#permalink] New post   26 Dec 2017, 07:01
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In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?

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\(\frac{86}{100}\)
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Re: In a town, 80% of the men are registered voters [#permalink] New post   26 Dec 2017, 11:03
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sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).
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Re: In a town, 80% of the men are registered voters [#permalink] New post   26 Dec 2017, 07:02
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This is a numeric entry question. Why the OA is A??

Please, review it.

Thank you
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Re: In a town, 80% of the men are registered voters [#permalink] New post   26 Dec 2017, 07:12
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Carcass wrote:
This is a numeric entry question. Why the OA is A??

Please, review it.

Thank you


The fraction of total that is men is 6/7 (Make a double matrix and solve it accordingly).
this is the answer I didnt have a file to upload
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 04:22
sandy wrote:
sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).


the stem doesn't indicate approximation, and the answer is 6/7, please check it out.
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 04:35
Peter wrote:
sandy wrote:
sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).


the stem doesn't indicate approximation, and the answer is 6/7, please check it out.




6/7 is actually = 86/100. So i guess sandy's answer is right.
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 04:35
sandy wrote:
sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).



thank you!
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 05:24
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sameer93 wrote:
sandy wrote:
sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).



thank you!


If the stem SPECIFICALLY indicates approximation, then 86/100 is correct.

The following is my calculation:

0.8m +0.66w= 0.78 (m+w)

then we got 0.8m+0.66w = 0.78m +0.78w

and we do some simplication here, we got 0.02m= 0.12w

and this means that 2m= 12w -----> m=6w

then m:w = 6:1

m/w+m(total population)= 6/7

is it clear now? no approximation invloved here. SO answer 6/7 would be better, never put approximation value if the stem doesn't specify.
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 05:57
Peter wrote:
sandy wrote:
sameer93 wrote:
In a town, 80% of the men are registered voters and 66% of the women are registered voters. if 78% of the total population is a registered voter, what fraction of the population is Men?


Let assume there are 100 people in town. Let \(x\) be the men and women \(100 - x\).

Total voters = 78% of 100 = 78.

Number of men voters = \(0.8 \times x\)
Number of women voters = \(0.66 \times (100 - x)= 66 - 0.66x\)

Total voters men and women = 0.14x + 66 = 78.

x= 12/ 0.14 = 86 approx.

Hence number of men is 86 and women is 14. Hence fraction of men in population is \(\frac{86}{100}\).


the stem doesn't indicate approximation, and the answer is 6/7, please check it out.


I don't understand would you like to explain it? :/
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 05:59
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[quote=

you can see the above illustration, otherwise, i don't know what to say.
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Dec 2017, 14:36
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@Peter is right in this regard. The stem DOES NOT mention (at all) approximation. Not only that, if you solve the question the solution is not approximate but is a known number and it is \(\frac{6}{7}\).

The problem even if it seems a word problem (it is indeed) can be solved like a mixture problem of two parts.

\(80 X + 66 Y = 78 (X + Y)\)

Solving the equation we obtain \(\frac{X}{Y} = \frac{6}{1}\).

Our X = 6 and the total of men + women are 6+1 = 7

So, the number of men is 6 over 7 or \(\frac{6}{7}\)
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In a town, 80% of the men are registered voters [#permalink] New post   Updated on: 28 Sep 2022, 17:43
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:) The easiest way to solve this problem.
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Originally posted by AkmKawser on 27 Sep 2022, 00:32.
Last edited by AkmKawser on 28 Sep 2022, 17:43, edited 1 time in total.
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Sep 2022, 00:34
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I like it. Would be better to write the solution in text but I guess is fine either way :blushing:
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Re: In a town, 80% of the men are registered voters [#permalink] New post   27 Sep 2022, 18:46
I think the question should be re-worded, it should ask what percentage of the population that is registered to vote are men. If 78% is registered to vote, how do we know how to divvy up the remaining 22% of the population amongst men and women? Maybe I am mistaken?
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