GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2019, 07:03

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A road crew painted two black lines across a road as shown in the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57152
A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 04 Jun 2015, 04:25
3
13
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

58% (02:58) correct 42% (02:44) wrong based on 225 sessions

HideShow timer Statistics

Image
A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile 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:
2015-06-04_1523.png
2015-06-04_1523.png [ 22.58 KiB | Viewed 4243 times ]

_________________
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57152
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 08 Jun 2015, 05:55
1
7
Bunuel wrote:
Image
A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile 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:
2015-06-04_1523.png


MANHATTAN GMAT OFFICIAL SOLUTION:

When comparing fractional pieces of a whole, we must find a common denominator. In this case, the 1-mile stretch is divided in thirds, fifths, and eighths. The smallest common denominator of 3, 5, and 8 is 120. If the 1-mile 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.
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 23 Apr 2014
Posts: 20
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 05 Jun 2015, 11:15
6
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
General Discussion
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 04 Jun 2015, 06:38
2
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 1-mile 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
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One 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
User avatar
V
Joined: 02 Sep 2009
Posts: 57152
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 04 Jun 2015, 06:42
GMATinsight 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 1-mile 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:



Added the image. Thank you.
_________________
Manager
Manager
User avatar
Joined: 18 Nov 2013
Posts: 77
Concentration: General Management, Technology
GMAT 1: 690 Q49 V34
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 06 Jun 2015, 09:27
2
1
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
User avatar
V
Joined: 02 Sep 2009
Posts: 57152
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 08 Jun 2015, 05:57
Bunuel wrote:
Bunuel wrote:
Image
A road crew painted two black lines across a road as shown in the figure above, to mark the start and end of a 1-mile 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:
2015-06-04_1523.png


MANHATTAN GMAT OFFICIAL SOLUTION:

When comparing fractional pieces of a whole, we must find a common denominator. In this case, the 1-mile stretch is divided in thirds, fifths, and eighths. The smallest common denominator of 3, 5, and 8 is 120. If the 1-mile 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:
on-the-number-line-above-the-segment-from-0-to-1-has-been-104204.html
kim-finds-a-1-meter-tree-branch-and-marks-it-off-in-thirds-140038.html
if-the-successive-tick-marks-shown-on-the-number-line-above-144053.html
a-straight-pipe-1-yard-in-length-was-marked-off-in-fourths-145031.html
_________________
Intern
Intern
avatar
B
Joined: 24 Apr 2016
Posts: 30
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 14 Apr 2018, 08:48
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
Intern
Intern
avatar
Joined: 13 Jan 2019
Posts: 3
Re: A road crew painted two black lines across a road as shown in the  [#permalink]

Show Tags

New post 24 Jul 2019, 03:39
UJs wrote:
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


Posted from my mobile device
GMAT Club Bot
Re: A road crew painted two black lines across a road as shown in the   [#permalink] 24 Jul 2019, 03:39
Display posts from previous: Sort by

A road crew painted two black lines across a road as shown in the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne