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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 ## If a child is randomly selected from Columbus Elementary tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If a child is randomly selected from Columbus Elementary ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Magoosh If a child is randomly selected from Columbus Elementary School, what is the probability that the child will be a boy? 1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75. 2) There are 35 more boys than there are girls. OA C ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12431 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: If a child is randomly selected from Columbus Elementary School, what is the probability that the child will be a boy? 1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75. 2) There are 35 more boys than there are girls. Target question: What is the probability that the child will be a boy? This is a good candidate for rephrasing the target question. Let G = # of girls in the school Let B = # of boys in the school So, G + B = total number of children in the school So, P(selected child is a boy) = B/(G + B) REPHRASED target question: What is the value of B/(G + B)? Aside: Hereâ€™s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100 Statement 1: If 25 boys are removed from the school, the probability of selecting a boy will be 0.75. So, the number of boys = B - 25, and the total number of children = G + (B - 25) We can write: (B - 25)/(G + B - 25) = 3/4 Since we have a linear equation with TWO variables, there's no way to solve this equation for B and G. So, statement 1 is NOT SUFFICIENT If you're not convinced, consider these two CONFLICTING cases: Case a: B = 28 and G = 1. After 25 boys leave, there are 3 boys and 1 girl. So, P(boy) = 3/4 = 0.75, which satisfies statement 1. In this case, the answer to the REPHRASED target question is B/(G + B) = 28/(1 + 28) = 28/29 Case b: B = 31 and G = 2. After 25 boys leave, there are 6 boys and 2 girls. So, P(boy) = 6/8 = 0.75, which satisfies statement 1. In this case, the answer to the REPHRASED target question is B/(G + B) = 31/(2 + 31) = 31/33 Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: There are 35 more boys than there are girls. There are several CONFLICTING cases that satisfy statement 2. Here are two: Case a: B = 36 and G = 1. In this case, the answer to the REPHRASED target question is B/(G + B) = 36/(1 + 36) = 36/37 Case b: B = 37 and G = 2. In this case, the answer to the REPHRASED target question is B/(G + B) = 37/(2 + 37) = 37/39 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined From statement 1, we can write: (B - 25)/(G + B - 25) = 3/4 Cross multiply to get: 3(G + B - 25) = 4(B - 25) Expand: 3G + 3B - 75 = 4B - 100 Rearrange to get: 3G - B = - 25 From statement 2, we can write: B = G + 35 At this point, we have two different linear equations with two variables. So, we COULD solve the system for B and G, which means we COULD answer the REPHRASED target question with certainty. So, the combined statements are SUFFICIENT Answer: C 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 AAPL wrote: Magoosh If a child is randomly selected from Columbus Elementary School, what is the probability that the child will be a boy? 1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75. 2) There are 35 more boys than there are girls. $$? = {b \over {b + {\rm{g}}}}$$ $$\left( 1 \right)\,\,{{b - 25} \over {\left( {b - 25} \right) + g}} = {3 \over 4}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {28,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{28} \over {29}} \hfill \cr \,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {31,2} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{31} \over {33}} \ne {{28} \over {29}} \hfill \cr} \right.$$ $$\left( 2 \right)\,\,b = g + 35\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {36,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{36} \over {37}} \hfill \cr \,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {37,2} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{37} \over {39}} \ne {{36} \over {37}} \hfill \cr} \right.$$ $$\left( {1 + 2} \right)\,\,\,{{\left( {g + 35} \right) - 25} \over {\left[ {\left( {g + 35} \right) - 25} \right] + g}} = {3 \over 4}\,\,\,\,\mathop \Rightarrow \limits^{{1^{{\rm{st}}}}\,\,{\rm{degree}}} \,\,\,\,g\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,b\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$ 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! • Award-winning private GMAT tutoring Register now and save up to$200

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