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# In a 200 member association consisting of men and women

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Joined: 16 Dec 2018
Posts: 67
Re: In a 200 member association consisting of men and women  [#permalink]

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05 Dec 2019, 02:28
Bunuel wrote:
In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?

A) 49
B) 47
c) 45
D) 43
E) 41

Thanks

Let the # of women be $$w$$, then # of men will be $$200-w$$. We want to minimize $$0.25w+0.2(200-w)$$ --> $$0.25w+0.2(200-w)=0.05w+40=\frac{w}{20}+40$$, so we should minimize $$w$$, but also we should make sure that $$\frac{w}{20}+40$$ remains an integer (as it represent # of people). Min value of $$w$$ for which w/20 is an integer is for $$w=20$$ --> $$\frac{w}{20}+40=1+40=41$$.

Or: as there are bigger percentage of homeowner women then we should minimize # of women, but we should ensure that $$\frac{1}{4}*w$$ and $$\frac{1}{5}*(200-w)$$ are integers. So $$w$$ should be min multiple of 4 for which $$200-w$$ is a multiple of 5 (basically w should be min positive multiple of 20), which turns out to be for $$w=20$$.

Hope it's clear.

Bunuel
why do not we took at first For example: Let the # of men be $$m$$, then # of women will be $$200-m$$. if so after calculating i got answer 49? why this process goes to wrong answer?
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Re: In a 200 member association consisting of men and women  [#permalink]

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05 Dec 2019, 15:05
Hi hudacse6,

To start, there are additional pieces of information that you have to consider beyond that fact that there are 200 total people. We are also told that 20% of men and 25% of women are homeowners - and those are both specific fractions.

20% = 1/5, so we know that the number of men MUST be a multiple of 5
25% = 1/4, so we know that the number of women MUST be a multiple of 4

These facts tell us that M and W cannot be "any" numbers from 1-200, they can only be specific numbers AND the sum of those two numbers must add up to 200. In addition, we want the LEAST number of homeowners, meaning that we want to maximize the number of men (since a smaller percentage are homeowners) and minimize the number of women.

It's not clear whether you accounted for that additional information in your calculations. If you repost and include the 'steps' that you worked through, then we should be able to define why you did not get to the correct answer.

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Re: In a 200 member association consisting of men and women   [#permalink] 05 Dec 2019, 15:05

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