Bunuel wrote:

nades09 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

Please explain

Thanks

NAD

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 \(w=20\) --> \(\frac{w}{20}+40=1+40=41\).

Answer: E.

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.

Hi

Bunuel generis,

pushpitkc hope you are having nice weekend

please advise normally in MIN/MAX problems to find minimal value we need to MAXimize another value, right ?

you say "

We want to minimize \(0.25w+0.2(200-w)\) " why are you saying this "

we need to minimize" instead of this "

In order to minimize the number of homeowners we need to maximize number of non homeowners" shouldnt we maximize number of non homeowners in order to minimize number of homeowners ?

What do you minimize here and why are you subtracting number of women from 200 and not number of men ?

Also it says "exactly 20% of men and exactly 25 % women are homeowners"

this phrase does it mean tat there are total 25 % woman and all of them are homeowners ?

what is the diference between

exactly 20% of men and

exactly 25 % women what if the question were "In a 200 member association consisting of men and women, exactly 20% of men and exactly 25 %

of women are homeowners. What is the least number of members who are homeowners?

what would be the equation ?

And one more thing, let me copy and paste some MIN/MAX guidlines from this link, see below

https://gmatclub.com/forum/gmat-tip-of- ... l#p2058670Minimizing the highest value by maximizing the others

Maximizing the highest value by minimizing the othersMinimizing the lowest value by maximizing the others

Maximizing the lowest value by minimizing the othersaren't the above mentioned rules the same ? I mean two rules marked in red are the same as two rules marked in green

i would appreciate your explanation

thank you

UPDATE:) i think today i figured out answer to one of my questions:) human brain cosists of two parts VERBAL and QUANT, so i yesterday turmed on the wrong part of my brain to solve quant

so let me answer this question

you say "We want to minimize \(0.25w+0.2(200-w)\) " why are you saying this " we need to minimize" instead of this " In order to minimize the number of homeowners we need to maximize number of non homeowners"

so we duduct number of woman from 200 because we need to maximize number of non-homeowners and minimize number of homeowners

Now why do we deduct # of woman from 200 and not number of men ? well, because we know that 25% are woman and this will give us upportunity maximize # of non homeowners and minimize number of homeowners

0.2(200-w) here maximize # of non homeowners and minimize number of men homeowners

YAY! EUREKA !

Guys how about this method

if 25 % are woman and answer choices are within 40 - 49 range AND 20% of men are menhomeowners

than i could say that 25% of 200 is 40 and since i need to minimize number of men and only 20% of men are menhomeowners. then

total #of men is 5 and out of them

0.20*5 =1

hence 40+1 = 41

is it valid approach ?

Bunuel,

generis ,

pushpitkc