February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52971

A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
04 Jun 2015, 03:25
Question Stats:
59% (02:59) correct 41% (02:46) wrong based on 259 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
08 Jun 2015, 04:55
Bunuel wrote: A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway? (A) 0 (B) 1/120 (C) 1/60 (D) 1/40 (E) 1/30 Attachment: 20150604_1523.png MANHATTAN GMAT OFFICIAL SOLUTION:When comparing fractional pieces of a whole, we must find a common denominator. In this case, the 1mile stretch is divided in thirds, fifths, and eighths. The smallest common denominator of 3, 5, and 8 is 120. If the 1mile highway is divided into 120 equal increments, where will the red, white, and blue marks fall? Red (thirds): 40, 80 (out of 120 increments) White (fifths): 24, 48, 72, 96 (out of 120 increments) Blue (eighths): 15, 30, 45, 60, 75, 90, 105 (out of 120 increments) The smallest distance between two marks is 75 – 72 = 3 or 48 – 45 = 3. This equates to 3/120, or 1/40 miles. The correct answer is D.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 23 Apr 2014
Posts: 21

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
05 Jun 2015, 10:15
since iam not so good with decimals took the lcm of 8,5,3 which is 120 so if the length of the road is 120 the markings for 1/8 are 15,30,45,60,75,90,105,120 for 1/5 are 24, 48, 72,96 and 120. for 1/3 are 40, 80,120 so the min difference is between 48  45=3 sinc3e the distance is to be found in 1 mile so the ans is 3/120 =1/40 hence D




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2788
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
04 Jun 2015, 05:38
Bunuel wrote: A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway?
(A) 0 (B) 1/120 (C) 1/60 (D) 1/40 (E) 1/30 Although I couldn't see any given Figures however the solution is as mentioned below:1/8 = 0.125 i.e. Markings will be at {.125, .25, .375, .5, .625, .75, .875}1/5 = 0.2 i.e. Markings will be at {.2, .4, .6, .8}1/3 = 0.33 i.e. Markings will be at {.33, .66)Let's say we have 1 mile stretch as mentioned below  (.125) (.2) (.25) (.33) (.375) (.4) (.5) (.6) (.625) (.66) (.75) (.8) (.875) The Set of all values become {.125, .2, .25, .33, .375, .4, .5, .6, .625, .66, .75, .8, .875} Hence the smallest possible difference between any two consecutive numbers will be the smallest piece cut and i.e. 0.4 0.375 = .025 = 25/1000 = 1/40 Answer: Option
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
04 Jun 2015, 05:42



Manager
Joined: 18 Nov 2013
Posts: 78
Concentration: General Management, Technology

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
06 Jun 2015, 08:27
red line at each third of a mile = \(\frac{1}{3} , \frac{2}{3} , \frac{3}{3}.\) white line at each fifth of a mile = \(\frac{1}{5} , \frac{2}{5} , \frac{3}{5} , \frac{4}{5} , \frac{5}{5}.\) blue line at each eighth of a mile = \(\frac{1}{8} , \frac{2}{8} , \frac{3}{8} , \frac{4}{8} , \frac{5}{8} ,\frac{6}{8} ,\frac{7}{8} ,\frac{8}{8}.\) LCM of all three Denominators = 3 * 5 * 8 = 120 (I prefer the LCM approach too ,makes it much simpler to look at these numbers, + that's how answers are written too)red line at each third of a mile = \(\frac{40}{120} , \frac{80}{120} , \frac{120}{120}.\)
white line at each fifth of a mile = \(\frac{24}{120} , \frac{48}{120} , \frac{72}{120} , \frac{96}{120} , \frac{120}{120}.\)
blue line at each eighth of a mile = \(\frac{15}{120} , \frac{30}{120} , \frac{45}{120} , \frac{60}{120} , \frac{75}{120} ,\frac{90}{120} ,\frac{105}{120} ,\frac{120}{120}.\) look at the options that are closest to each other (\(\frac{48}{120}\), \(\frac{45}{120}\) ) and (\(\frac{72}{120}\) ,\(\frac{75}{120}\) ) closest with difference of = \(\frac{3}{120}\) = \(\frac{1}{3}\) Ans: D
_________________
_______  Cheers
+1 kudos if you like



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
08 Jun 2015, 04:57
Bunuel wrote: Bunuel wrote: A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1mile stretch. Between the two black lines, they will paint across the road a red line at each third of a mile, a white line at each fifth of a mile, and a blue line at each eighth of a mile. What is the smallest distance (in miles) between any of the painted lines on this stretch of highway? (A) 0 (B) 1/120 (C) 1/60 (D) 1/40 (E) 1/30 Attachment: 20150604_1523.png MANHATTAN GMAT OFFICIAL SOLUTION:When comparing fractional pieces of a whole, we must find a common denominator. In this case, the 1mile stretch is divided in thirds, fifths, and eighths. The smallest common denominator of 3, 5, and 8 is 120. If the 1mile highway is divided into 120 equal increments, where will the red, white, and blue marks fall? Red (thirds): 40, 80 (out of 120 increments) White (fifths): 24, 48, 72, 96 (out of 120 increments) Blue (eighths): 15, 30, 45, 60, 75, 90, 105 (out of 120 increments) The smallest distance between two marks is 75 – 72 = 3 or 48 – 45 = 3. This equates to 3/120, or 1/40 miles. The correct answer is D.Similar question to practice: onthenumberlineabovethesegmentfrom0to1hasbeen104204.htmlkimfindsa1metertreebranchandmarksitoffinthirds140038.htmlifthesuccessivetickmarksshownonthenumberlineabove144053.htmlastraightpipe1yardinlengthwasmarkedoffinfourths145031.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 24 Apr 2016
Posts: 30

Re: A road crew painted two black lines across a road as shown in the
[#permalink]
Show Tags
14 Apr 2018, 07:48
Not sure if this works...but this is how I approached this question.
We have paint in 1/3, 1/5, and 1/8 increments. The smallest distance between two lines has to have a denominator that is at most the denominator of two of these increments (e.g. 5*3=15, 8*3 = 24, 8*5 = 40). I say at most because we may be able to reduce the fraction.
A clearly can't be the answer, and using the logic above B and C cannot be the answer as well. Now I pick multiples of (1/8) and multiples of (1/5) to see if (1/40) works. If I have a denominator of 40, then for (1/5) I'm looking at intervals of 8, 16, 24, 32, 40. And for 1/8 I'm looking for intervals of 5, 10, 15, 20, 25, 30, 35, 40. As you can see this works for 16/40 (which is 2/5) and 15/40 (which is 3/8). (D)
(A) 0 (B) 1/120 (C) 1/60 (D) 1/40 (E) 1/30




Re: A road crew painted two black lines across a road as shown in the
[#permalink]
14 Apr 2018, 07:48






