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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 ## Last Problem in OG12 Diagnostic ##### This topic has 5 expert replies and 6 member replies ## Last Problem in OG12 Diagnostic 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) OA: [spoiler]C[/spoiler] Legendary Member Joined 28 Dec 2008 Posted: 1578 messages Followed by: 9 members Upvotes: 82 GMAT Score: 720 okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) Let he takes p hours going and t-p hours coming px = (t-p)*y =>px+py = ty so p = ty/x+y so px = txy/x+y _________________ Charged up again to beat the beast Master | Next Rank: 500 Posts Joined 07 Apr 2009 Posted: 180 messages Followed by: 2 members Upvotes: 5 Test Date: Sept 11 Target GMAT Score: 700+ GMAT Score: ~660 okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) OA: C Pick numbers X = 4 Y = 2 T = 1 hour running, 2 hours walking = 3. How many hours can Aaron spend running. Well, if he spends one hour jogging and 2 hours walking then he will just jog a total of 4 miles. So find 4. A. 12/ 2 = 6 - NO B. 7 / 6 = NO C. 24/ 6 = YES D = 9 / 6 = NO E = 5 / something that isn't 1.25 C Wins. Master | Next Rank: 500 Posts Joined 26 Nov 2010 Posted: 139 messages Followed by: 1 members Upvotes: 20 Test Date: Feb 3, 2011 GMAT Score: 720 OK, perhaps the easiest way to answer is to look at the units of the options. Question is - how many miles, so the answer must have units of distance. (a) has unit of time (b) is adding distance and time in the numerator, which cannot be true (c) has unit of distance - (speed*speed*time/speed = speed*time = distance) (d) same explanation as b (e) two quantities have different units, on top of the presence of errors of choice b ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Hi there! Let z be the number we are looking for: # of miles jogging or walking ("... same route"). From Units Control, we know that miles over mph gives hour, therefore the "hour-unit equation " is: z/x + z/y = t , therefore z(1/x + 1/y)=t hence z = (txy)/(x+y) and we are done. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Senior | Next Rank: 100 Posts Joined 11 Dec 2010 Posted: 56 messages Upvotes: 3 The average speed for Aaron's entire trip is 2xy/(x+y). The total distance traveled d, at an average speed is 2xy/(x+y) * t d = 2xyt/(x+y). The question asks what is the distance Aaron has to travel jogging, one way from his home, which is basically d/2 Hence d/2 = xyt/(x+y) Since i have considered the average speed, it does not matter jogging or walking. Hope this helps. Newbie | Next Rank: 10 Posts Joined 02 Dec 2011 Posted: 1 messages I really like how you all have tackled this problem in a different way... it really highlights the agility of mathematical minds!! I wanted to ask you, Fabio, how you went from z(1/x +1/y) = t to z = (txy)/(x+y). I got stuck trying to carry that algebra out. Thank-you! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15359 messages Followed by: 1865 members Upvotes: 13060 GMAT Score: 790 okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) OA: C Let the distance = 10 miles. Let x = 5 miles per hour and y = 2 miles per hour. Then t = total travel time = 10/5 + 10/2 = 7. Since the question asks for the distance, our target is 10. Now we plug x=5, y=2 and t=7 into the answers to see which yields our target of 10. Only answer choice C works: (xyt)/(x+y) = (5*2*7)/(5+2) = 10. The correct answer is C. _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 rene26 wrote: I really like how you all have tackled this problem in a different way... it really highlights the agility of mathematical minds!! I wanted to ask you, Fabio, how you went from z(1/x +1/y) = t to z = (txy)/(x+y). I got stuck trying to carry that algebra out. Thank-you! Hi, rene26, thanks for your interest in my solution. Please note that: (1) if (say) A = 1/x + 1/y = (x+y)/xy , then (2) 1/A = (1/x + 1/y)^(-1) = xy/(x+y) , (3) therefore z = t/A = t*(1/A) = (txy)/(x+y) and we are done. Regards, FÃ¡bio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Senior | Next Rank: 100 Posts Joined 13 Oct 2015 Posted: 55 messages okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) OA: C Here you go for this solution. https://gmatclub.com/forum/aaron-will-jog-from-home-at-x-miles-per-hour-and-then-walk-back-home-135828-20.html#p2260928 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12995 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach. Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier. However, the algebraic approach isn't too bad. Let's let d = the number of miles (distance) that Aaron jogs. This means that d also = the distance that Aaron walks. Let's start with a WORD EQUATION: total time = (time spent jogging) + (time spent walking) In other words: t = (time spent jogging) + (time spent walking) Since time = distance/speed, we can write: t = d/x + d/y [our goal is to solve this equation for d] The least common multiple of x and y is xy, so we can eliminate the fractions by multiplying both sides by xy. When we do so, we get... txy = dy + dx Factor right side to get: txy = d(x + y) Divide both sides by (x+y) to get: txy/(x+y) = d So, the correct answer is C 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 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 okigbo wrote: 24. Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking? a) xt/y b) x+t/xy c) xyt/x+y d) (x+y+t)/xy e) ((y+t)/x)-(t/y) OA: C We can let d = the distance traveled on walking or jogging. Thus, the jogging time is d/x and the walking time is d/y. Since the total time is t: d/x + d/y = t Multiply the entire equation by xy: dy + dx = txy d(y + x) = txy d = txy/(y + x) Answer: C _________________ 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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