• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In a 200 member association consisting of men and women, exa ##### This topic has 5 expert replies and 0 member replies ### Top Member ## In a 200 member association consisting of men and women, exa ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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 OA E Last edited by BTGmoderatorDC on Wed Jan 16, 2019 6:58 am; edited 2 times in total ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC 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 Letting m = the number of men in the association and w = the number of women in the association, we know that: m + w = 200 m = 200 - w Thus: 0.2(200 - w) + 0.25w = homeowners 40 - 0.2w + 0.25w = homeowners 40 + 0.05w = homeowners 40 + w/20 = homeowners We see that w must be a multiple of 20 and since we want the least number of homeowners, w = 20. So the least number of homeowners is 40 + 20/20 = 40 + 1 = 41. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi All, We're told that in a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. We're asked for the LEAST number of members who are homeowners. This question is built around a couple of Number Properties - and to MINIMIZE the number of people who are homeowners, we have to MAXIMIZE the number of men in the group (since a smaller percentage of men are homeowners). To start, since 20% of men are homeowners, we know that the number of men MUST be a multiple of 5. In that same way, since 25% of women are homeowners, we know that the number of women MUST be a multiple of 4. Thus, we need to add the largest possible multiple of 5 to a multiple of 4 and get a total of 200, while accounting for the fact that there MUST be some men and some women. Logically, we can 'work down' from 200 to find those numbers. IF there were... 4 women, then there'd be 196 men (not valid; number of men needs to be a multiple of 5) 8 women, then there'd be 192 men (not valid; number of men needs to be a multiple of 5) Etc. With a little more work, you'll find that 20 women and 180 men is situation that is needed. From there the LEAST possible number of homeowners would be... (.25)(20) + (.2)(180) = 5 + 36 = 41 homeowners Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12981 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC 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 In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let's see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are homeowners, then the number of male homeowners = 20% of 199 = 39.8. This makes no sense, since we can't have 39.8 men. Likewise, if 25% (aka 1/4) of the women are homeowners, then the number of female homeowners = 25% of 1 = 0.25. This makes no sense either. Let's now focus on the women. We know that, in order to have an INTEGER number of female homeowners, the number of females must be divisible by 4. Likewise, in order to have an INTEGER number of male homeowners, the number of females must be divisible by 5. So, the first pair of values that meet the above conditions are: 180 men and 20 women. 20% of 180 = 36, so there are 36 male homeowners. 25% of 20 = 5, so there are 5 female homeowners. MINIMUM number of homeowners = 36 + 5 = 41 Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Consider the following equation: 7x + 5y = 70. If x and y are nonnegative integers, the following solutions are possible: x=10, y=0 x=5, y=7 x=0, y=14. Notice the following: The value of x changes in increments of 5 (the coefficient for y). The value of y changes in increments of 7 (the coefficient for x). This pattern will be exhibited by any fully reduced equation that has two variables constrained to nonnegative integers. BTGmoderatorDC 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 . Since only 1/5 of men own homes -- versus 1/4 of women -- the number of homeowners will be minimized if we MAXIMIZE THE NUMBER OF MEN. Let x = the number of male homeowners. Since 1/5 of the men own homes, the total number of men must be 5 times the number of male homeowners = 5x. Let y = the number of female homeowners. Since 1/4 of the women own homes, the total number of women must be 4 times the number of female homeowners = 4y. Since there are 200 members in total, we get: 5x + 4y = 200. Nonnegative integral solutions for the equation in blue, in accordance with the pattern discussed above: x=40, y=0 x=36, y=5 x=32, y=10 And so on. Since x and y must both be positive, the option in red is not viable. Implication: To maximize the value of x and thus the total number of men, we must assign x and y the combination in green: x=36 and y=5, with the result that the total number of homeowners = 36+5 = 41. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2094 messages Followed by: 238 members Upvotes: 1443 OP, are you sure this is an OG question? Which edition of the OG did you get this problem from? It's not in any edition I own. A google search yields only 1 post from gmatclub, and 3 posts on this forum - all posted by you in the last month. The wording of this problem does not sound like an OG problem. Any OG problem asking us to minimize or maximize would stipulate "what is the least POSSIBLE number..." It is also missing "25% of women." This unfortunately has the effect of casting doubt on the veracity of your sources. BTGmoderatorDC 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 OA E Source: Official Guide _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

199 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts