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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 ## How much time did it take a certain car to travel 400 ##### This topic has 3 expert replies and 0 member replies ### Top Member ## How much time did it take a certain car to travel 400 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did. OA B Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12833 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did. Target question: How long did it take to travel 400km To find the travel time, we need to know the average speed traveled. Let x = the average speed traveled. REPHRASED target question: What is the value of x? Statement 1: The car traveled the first 200 km in 2.5 hrs No info about the 2nd half of the trip, so we can't determine the overall average speed (aka x). Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT Statement 2: If the carâ€™s average speed had been 20 km/h faster, it would have traveled the 400 km in 1 hour less time. Let's start with a word equation: (travel time at x km/h) - 1 = (travel time at x+20 km/h) Since time = distance/speed, we can now write: (400/x) - 1 = 400/(x+20) IMPORTANT: At this point, we need only determine whether this equation will yield 1 or 2 valid values of x. If it yields only 1 valid value, then statement 2 is sufficient. If it yields 2 valid values, then statement 2 is not sufficient. Rewrite as: (400-x)/x = 400/(x+20) Cross multiply: (400)(x) = (400-x)(x+20) Simplify: 400x = 8000 + 380x - xÂ² Rewrite: xÂ² + 20x - 8000 = 0 Factor: (x + 100)(x - 80) = 0 So, x = -100 or 80 Since x cannot be negative, it must be the case that x = 80 Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT Answer: B 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: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did. Source: GMAT Prep $$400\,{\rm{km}}\,\,\,\,\,\left\{ \matrix{ \,\,\left( {{\rm{real}}\,\,{\rm{speed}}\,,\,\,{\rm{real}}\,\,{\rm{time}}} \right)\,\,\,{\rm{ = }}\,\,\,\left( {{V_R}\,\,,\,\,{T_R}} \right) \hfill \cr \,\,\left( {{\rm{hypothetical}}\,\,{\rm{speed}}\,,\,\,{\rm{hypothetical}}\,\,{\rm{time}}} \right)\,\,\,{\rm{ = }}\,\,\,\left( {{V_H}\,\,,\,\,{T_H}} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\,\,\,\left[ {\,{{{\rm{km}}} \over {\rm{h}}}\,} \right]\,\,\,,\,\,\,\,\left[ {\,{\rm{h}}\,} \right]\,\,\,} \right)$$ $$? = {T_R}\,\,\,\left[ {\rm{h}} \right]$$ $$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{If}}\,\,{\rm{it}}\,\,{\rm{took}}\,\,0.5\,{\rm{h}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{last}}\,\,200\,{\rm{km}}\,\,\,\,\, \Rightarrow \,\,\,\,?\,\, = \,\,3\, \hfill \cr \,{\rm{If}}\,\,{\rm{it}}\,\,{\rm{took}}\,\,1\,{\rm{h}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{last}}\,\,200\,{\rm{km}}\,\,\,\,\, \Rightarrow \,\,\,\,?\,\, = \,\,3.5\,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,{V_H} = {V_R} + 20\,\,\,\left( * \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{T_R} - {T_H} = 1\,\,\,\,\,\,\left[ {\rm{h}} \right]$$ Now itÂ´s time for UNITS CONTROL, one of the most powerful tools of our method: $${{{\rm{km}}} \over {\,\,\,{{{\rm{km}}} \over {\rm{h}}}\,\,}} = {\rm{h}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{ {T_R} = {{400} \over {{V_R}}} \hfill \cr {T_H}\,\mathop = \limits^{\left( * \right)} \,\,{{400} \over {{V_R} + 20}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,{{400} \over {{V_R}}} - {{400} \over {{V_R} + 20}} = 1$$ $${{400\left( {{V_R} + 20} \right)} \over {{V_R}\,\,\left( {{V_R} + 20} \right)}} - {{400\,\,{V_R}} \over {\left( {{V_R} + 20} \right)\,\,{V_R}}} = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,400 \cdot 20 = {V_R}\,\,\left( {{V_R} + 20} \right)$$ $${V_R}^2 + 20{V_R} - 400 \cdot 20 = 0\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{of}}\,\,{\rm{roots}}}^{{\rm{product}}} \,\,\,\,\,\,\,\left( {{c \over a} = } \right)\,\,\,{{ - 400 \cdot 20} \over 1} < 0\,\,\,\, \Rightarrow \,\,\,\,\,{V_R}\, > 0\,\,\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,$$ $$\left( {\,\,\,\left. \matrix{ {V_R}\,\,{\rm{unique}}\,\, \hfill \cr {\rm{400}}\,{\rm{km}} \hfill \cr} \right\}\,\,\,\, \Rightarrow \,\,\,\,\,? = \,\,{T_R}\,\,\,{\rm{unique}}\,\,\,} \right)$$ 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 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1898 messages Followed by: 30 members Upvotes: 470 BTGmoderatorDC wrote: How much time did it take a certain car to travel 400 kilometers? (1) The car traveled the first 200 kilometers in 2.5 hours. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did. OA B Source: GMAT Prep Question: How much time did it take a certain car to travel 400 kilometers? Let's take each statement one by one. (1) The car traveled the first 200 kilometers in 2.5 hours. Certainly insufficient since we do not know how much it took to travel the remaining 200 kms. Insufficient. (2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did. Say the average speed is x kmps. Thus, time taken to travel 400 kms @x kmph = 400/x hours Time taken to travel 400 kms @(x + 20) kmph = 400/(x + 20) hours => 400/x - 400/(x + 20) = 1 => 8000 = x(x + 20) We see that 8000 is a product of two positive integers that are 20 away from each other. Upon hit and trial, we see that if we write 8000 as 80*100, we have 80*(80 + 20). Thus, x = 80 kmph. Sufficient. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | New Delhi | Seoul | Cairo | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! 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