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In a country, 60% of the male citizen and 70% of the female citizen ar

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In a country, 60% of the male citizen and 70% of the female citizen ar [#permalink]

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In a country, 60% of the male citizen and 70% of the female citizen are eligible to vote. 70% of male citizens eligible to vote voted, and 60% of female citizens eligible to vote voted. What fraction of the citizens voted during the election?

(A) 0.42

(B) 0.48

(C) 0.49

(D) 0.54

(E) 0.60
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Re: In a country, 60% of the male citizen and 70% of the female citizen ar [#permalink]

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Let us say total men in the country is represented by 100m
Let us say total women in the country is represented by 100W

Men Eligible to vote = 60% of 100m = 60m
Women Eligible to vote 70% of 100w = 70w

Men actually voted = 70% of 60m = 42m
Women actually voted = 60% of 70w = 42w

Total men and women voted = 42m + 42w = 42(m+w)
Total population= 100m +100w = 100(m+w)

fraction of the citizens voted during the election = 42(m+w)/100(m+w) = 0.42

Answer is A
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Re: In a country, 60% of the male citizen and 70% of the female citizen ar [#permalink]

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New post 06 Mar 2017, 20:48
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vikasp99 wrote:
In a country, 60% of the male citizen and 70% of the female citizen are eligible to vote. 70% of male citizens eligible to vote voted, and 60% of female citizens eligible to vote voted. What fraction of the citizens voted during the election?

(A) 0.42

(B) 0.48

(C) 0.49

(D) 0.54

(E) 0.60



"60% of the male citizen are eligible to vote and 70% of those eligible, voted" - So 70% of 60% = 42% of total males voted

"70% of the female citizen are eligible to vote and 60% of those eligible, voted" - So 60% of 70% = 42% of total females voted

It doesn't matter how many of the total are males and how many are females. Since 42% of both voted, 42% of the citizens voted.

Answer (A)

Note that had we obtained different values for "% of total males who voted" and "% of total females who voted", we would not have been able to say the % of total citizens who voted. It would depend on what percentage of the total citizens are male/female.

To take a simple case, say
40% of total males voted
50% of total females voted

If the population has all males, 40% of the citizens voted.
If the population has all females, 50% of the citizens voted.
Depending on the proportion of males/females in the population, the percentage of citizens who voted changes.
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Re: In a country, 60% of the male citizen and 70% of the female citizen ar [#permalink]

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New post 10 Mar 2017, 09:27
vikasp99 wrote:
In a country, 60% of the male citizen and 70% of the female citizen are eligible to vote. 70% of male citizens eligible to vote voted, and 60% of female citizens eligible to vote voted. What fraction of the citizens voted during the election?

(A) 0.42

(B) 0.48

(C) 0.49

(D) 0.54

(E) 0.60


We can let m = the number of male citizens and f = the number of female citizens in this country. So there are (m + f) citizens in this country.

From the information given in the problem, we see that 0.6m male citizens and 0.7f female citizens are eligible to vote. Furthermore, 0.7(0.6m) = 0.42m male citizens and 0.6(0.7f) = 0.42f female citizens voted.

Therefore, a total of (0.42m + 0.42f) citizens voted. The fraction of the citizens who voted is:

(0.42m + 0.42f)/(m + f) = 0.42(m + f)/(m + f) = 0.42

Answer: A
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Re: In a country, 60% of the male citizen and 70% of the female citizen ar   [#permalink] 10 Mar 2017, 09:27
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