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M02-10

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M02-10  [#permalink]

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New post 15 Sep 2014, 23:17
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A
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D
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Difficulty:

  15% (low)

Question Stats:

81% (01:27) correct 19% (01:24) wrong based on 173 sessions

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In Town X, \(\frac{2}{3}\) of the males and \(\frac{3}{5}\) of the females speak Spanish. If the ratio of females to males in the town is 2:3, what percentage of the total population in Town X speaks Spanish?

A. 36%
B. 40%
C. 48%
D. 64%
E. 73%

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Re M02-10  [#permalink]

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New post 15 Sep 2014, 23:17
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Official Solution:

In Town X, \(\frac{2}{3}\) of the males and \(\frac{3}{5}\) of the females speak Spanish. If the ratio of females to males in the town is 2:3, what percentage of the total population in Town X speaks Spanish?

A. 36%
B. 40%
C. 48%
D. 64%
E. 73%


Assume that the total population of Town X is 100.

The ratio of females to males in the town is 2:3. Since we picked 100 for the population, the number of females is 40 and the number of males is 60.

Out of 40 females, \(\frac{3}{5}\) speak Spanish. That is, \(\frac{3}{5}*40 = 24\) females speak Spanish.

Out of 60 males, \(\frac{2}{3}\) speak Spanish. That is, \(\frac{2}{3}*60 = 40\) males speak Spanish.

So, a total of \(24 + 40 = 64\) people out of 100 speak Spanish. Thus, the answer is 64%.


Answer: D
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Re M02-10  [#permalink]

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New post 19 Mar 2015, 01:34
I think this question is good and helpful.
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M02-10  [#permalink]

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New post 11 Aug 2015, 20:34
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Another way to solve this is to recognize that 66.6% of males and 60% of Females speak Spanish. The % of total population speaking Spanish has to be between these 2 values. We can eliminate all options which do not fall in the range 60% to 66.6%.
@Bunuel...pls let me know whether this approach is correct.
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Re: M02-10  [#permalink]

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New post 26 Dec 2015, 06:06
Bunuel

Can we apply weighted average technique here?

The 2/3 of the males and 3/5 of the females speak Spanish.Then total population in Town X speaks Spanish
will be between 66.6% to 60%
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Re: M02-10  [#permalink]

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New post 02 Apr 2018, 09:12
I solved it using fractions.

(%M speaking Spanish)(%M) + (%F speaking Spanish)(%F) = Total % Speaking Spanish
(3/5)(2/3)+(2/5)(3/5) = 16/25 = 64/100
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Re: M02-10 &nbs [#permalink] 02 Apr 2018, 09:12
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