M02-10

Question

In Town X,  \frac{2}{3}  of the male population and  \frac{3}{5}  of the female population 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%

Bunuel · Accepted Answer

Official Solution:

In Town X,  \frac{2}{3}  of the male population and  \frac{3}{5}  of the female population 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%

Let's assume that the total population of Town X is 100 people.
 
Given the ratio of females to males in the town is 2:3, and with a population of 100, we can deduce there are 40 females and 60 males.
 
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.
 
Therefore, a total of  24 + 40 = 64  out of 100 residents in Town X speak Spanish, which is 64% of the population.

Answer: D

IonutCZ · Answer

I think this question is  good  and  helpful .

Success2015 · Answer

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.

CPGguyMBA2018 · Answer

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

AirDime · Answer

The question is made too simple by the answer choices. It's easy to guess D because it is the only answer that falls between 2/3 (~67%) and 3/5 (60%) - the answer has to be within that range, given the constraints in the problem. The answer choices could have been something like 60%, 67%, 64%, 62% and 68%, which would have forced people to actually do the calculation.

AndrewN · Answer

Hello,  AirDime . I would argue that a key component to any PS question is understanding the available information in the answer choices, and sometimes official questions do, in fact, isolate correct answers in obvious fashion to anyone who knows how to spot them. If you got the question right in 30 seconds or so, good job, but looking at the statistics to the question, if 2:02 is the average time it has taken most question-answerers to arrive at the same conclusion, then many such people might not be as attuned to the test as you may be. This is not to even mention the number of people who missed the question. Perhaps you could share your approach, particularly if it is unique, to help the community, rather than take the time to post nothing more than a criticism.

Good luck with your studies.

- Andrew

AirDime · Answer

Thanks for the feedback, Andrew. Apologies for my tone; I was trying to point out a way to make the question more difficult.

AndrewN · Answer

No worries. And trust me, no one can accuse   Bunuel   of not knowing how to write tough questions! I am guessing that this one was created to test a particular Quant concept within a certain projected level of difficulty, nothing more. Full confession: Although I typically look to the answers first, I did not spot the obvious solution to this question myself, but took about a minute and a half to work out the problem in my head before committing to (D). Sometimes the fastest way eludes just about anyone.

The goal is always to help the community.

- Andrew

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

kouassidrissa047 · Answer

I like the solution - it’s helpful.

M02-10

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