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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 ## A certain family has 3 sons: Richard is 6 years older than D ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A certain family has 3 sons: Richard is 6 years older than D ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago? (A) 8 (B) 10 (C) 12 (D) 14 (E) 16 OA B Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago? (A) 8 (B) 10 (C) 12 (D) 14 (E) 16 We can create the equations: R = D + 6 and D = S + 8 So we have R = (S + 8) + 6 or R = S + 14. We are also given that in 8 years, Richard will be twice as old as Scott. We express Richardâ€™s age in 8 years as (R + 8) and Scottâ€™s age in 8 years as (S + 8), so we have: R + 8 = 2(S + 8) S + 14 + 8 = 2S + 16 6 = S Therefore, Scott is currently 6 years old and David is 6 + 8 = 14 years old. So 4 years ago, David was 10 years old. Answer: B _________________ 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 GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 4 years ago? (A) 8 (B) 10 (C) 12 (D) 14 (E) 16 Source: Princeton Review $$? = D - 4$$ $$R = D + 6\,\,\,\,\mathop \Rightarrow \limits^{ + \,8} \,\,\,\,\,R + 8 = D + 14\,\,\,\left( 1 \right)$$ $$D = S + 8\,\,\,\left( 2 \right)$$ $$R + 8 = 2\left( {S + 8} \right)\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right),\left( 2 \right)} \,\,\,D + 14 = 2D\,\,\,\, \Rightarrow \,\,\,\,14 = D$$ $$? = 10$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Junior | Next Rank: 30 Posts Joined 03 Oct 2018 Posted: 10 messages Let R, D and S be the present ages of Richard, David and Scott respectively. Therefore we can formulate the given equations from the data given R=D+8 D=S+8 Also after 8 years, Richard will be twice as old as Scott, giving us the equation R+8=(S+8) Solving these 3 equations , we get D=14 Thus, the age of David 4 years ago would be 10. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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