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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 2 expert replies and 1 member reply ### 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 Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12433 messages Followed by: 1244 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 OA E Source: Official Guide 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 our video course along with Sign up for our free Question of the Day emails And check out all of our 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 09 Oct 2010 Posted: 986 messages Followed by: 27 members Upvotes: 59 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 Source: Official Guide Excellent opportunity for the grid (aka double-matrix)! Important: we have chosen the blue expression wisely and the others follow from it. (Justify all of them!) $$? = {\left( {50 - M} \right)_{\min }}$$ $$\left( {50 - M} \right)\,\,{\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,\,\,M\,\,{\mathop{\rm int}}$$ $$\left( {10 - M} \right) \ge 1\,\,{\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,M \le 9\,\,{\mathop{\rm int}}$$ $$? = {\left( {50 - M} \right)_{\min }}\,\,\, = 41\,\,\,\,\left( {M = 9} \right)$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### Top Member Newbie | Next Rank: 10 Posts Joined 06 Dec 2018 Posted: 7 messages Easiest approach here is trial and error. Pick the lowest number (41) and put it into equation (1) M + W = 200 (2) $$\frac{1}{5}M+\frac{1}{4}W\ =\ 41$$ Thus you get W = 20 and M = 160; which are valid numbers. Since this is the lowest answer... Answer = 41 • FREE GMAT Exam Know how you'd score today for$0

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