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Intern Joined: 06 Oct 2017
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In a town, 80% of the men are registered voters [#permalink] 00:00

Question Stats: 50% (02:02) correct 50% (01:57) wrong based on 4 sessions
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?

[Reveal] Spoiler: OA
$$\frac{86}{100}$$
Moderator  Joined: 18 Apr 2015
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Re: In a town, 80% of the men are registered voters [#permalink]
Expert's post
This is a numeric entry question. Why the OA is A??

Thank you
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Intern Joined: 06 Oct 2017
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Re: In a town, 80% of the men are registered voters [#permalink]
Carcass wrote:
This is a numeric entry question. Why the OA is A??

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 GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: In a town, 80% of the men are registered voters [#permalink]
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Expert's post
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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Sandy
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Manager Joined: 27 Sep 2017
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Re: In a town, 80% of the men are registered voters [#permalink]
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.
Intern Joined: 06 Oct 2017
Posts: 9
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Kudos [?]: 3 , given: 2

Re: In a town, 80% of the men are registered voters [#permalink]
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.
Intern Joined: 06 Oct 2017
Posts: 9
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Kudos [?]: 3 , given: 2

Re: In a town, 80% of the men are registered voters [#permalink]
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! Manager Joined: 27 Sep 2017
Posts: 112
Followers: 1

Kudos [?]: 30  , given: 4

Re: In a town, 80% of the men are registered voters [#permalink]
1
KUDOS
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.
Intern Joined: 06 Oct 2017
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Kudos [?]: 3 , given: 2

Re: In a town, 80% of the men are registered voters [#permalink]
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? :/ Manager Joined: 27 Sep 2017
Posts: 112
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Re: In a town, 80% of the men are registered voters [#permalink]
1
KUDOS
[quote=

you can see the above illustration, otherwise, i don't know what to say.
Moderator  Joined: 18 Apr 2015
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Re: In a town, 80% of the men are registered voters [#permalink]
Expert's post
@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 $$\frac{6}{7}$$
_________________ Re: In a town, 80% of the men are registered voters   [#permalink] 27 Dec 2017, 14:36
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