GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Aug 2020, 15:35

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In a 200 member association consisting of men and women

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
B
Joined: 16 Dec 2018
Posts: 67
Re: In a 200 member association consisting of men and women  [#permalink]

Show Tags

New post 05 Dec 2019, 02:28
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.


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?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 17272
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a 200 member association consisting of men and women  [#permalink]

Show Tags

New post 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.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: In a 200 member association consisting of men and women   [#permalink] 05 Dec 2019, 15:05

Go to page   Previous    1   2   3   [ 42 posts ] 

In a 200 member association consisting of men and women

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne