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

It is currently 23 Jun 2018, 16:24
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

Two boys start cycling around a circular track in opposite directions

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Manager
Manager
avatar
S
Joined: 23 Sep 2016
Posts: 230
Premium Member Reviews Badge
Two boys start cycling around a circular track in opposite directions [#permalink]

Show Tags

New post 08 Mar 2018, 04:17
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

51% (01:37) correct 49% (01:47) wrong based on 79 sessions

HideShow timer Statistics

Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?

A. 15
B. 30
C. 60
D. 90
E. 120

SOURCE EXPERTSGLOBAL
Spoiler: OA
Manager
Manager
avatar
S
Joined: 23 Sep 2016
Posts: 230
Premium Member Reviews Badge
Re: Two boys start cycling around a circular track in opposite directions [#permalink]

Show Tags

New post 08 Mar 2018, 04:26
1
rishabhmishra wrote:
Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?
A. 15
B. 30
C. 60
D. 90
E. 120
SOURCE EXPERTSGLOBAL

SOLU lets first find out when they both will meet
as we all know both cyclist are coming towards each other they will meet soon so total distance must be divided by sum of their speed.
total distance will be 400 meters circumference of circle
so 400/10+5= 400/15
=80/3 in every 80/3 seconds they will meet
so in 40 min they will meet
40*60(convert in seconds)
we will divide total time with they took time to meet once so to identify how many times they met.
40*60*3/80
=90
so OA IS D
VP
VP
avatar
G
Joined: 07 Dec 2014
Posts: 1020
Two boys start cycling around a circular track in opposite directions [#permalink]

Show Tags

New post 08 Mar 2018, 12:25
rishabhmishra wrote:
Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?

A. 15
B. 30
C. 60
D. 90
E. 120

SOURCE EXPERTSGLOBAL


400m/15 combined mps=26 2/3 seconds until first crossing
40 min*60 sec=2400 seconds
2400/(26 2/3)=90 crossings
D
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1763
Premium Member CAT Tests
Two boys start cycling around a circular track in opposite directions [#permalink]

Show Tags

New post 11 Mar 2018, 16:09
1
rishabhmishra wrote:
Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?

A. 15
B. 30
C. 60
D. 90
E. 120

SOURCE EXPERTSGLOBAL

Find combined rate per minute. (R + R). Find time required to cross paths one time (D/R).
Finally, divide total time by time per crossing. Answer equals the # of times they meet.

Convert seconds to minutes

If time units are different, you can convert X seconds to one minute. Multiply the rate's number of seconds by N to get to 60 seconds. Multiply the numerator by N, too.

Rate of Boy 1:
\((\frac{10m}{1sec}*\frac{60}{60})=(\frac{600m}{60secs})=\frac{600m}{1min}\)

Rate of Boy 2:
\((
\frac{5m}{1sec})=(\frac{300m}{60secs})=\frac{300m}{1min}\)

Add rates

When travelers move in opposite directions, whether towards or away from one another, add rates (speeds). Combined rate:

\(\frac{600m}{1min} + \frac{300m}{1min}=\frac{900m}{1min}\)

Time it takes for them to cross paths once?

\(R*T = D\), so \(T=\frac{D}{R}\)

\(T=\frac{400m}{900\frac{meters}{minute}}=\frac{400}{900}mins=\frac{4}{9}min\)

for them to meet once

Number of times they cross/meet?

\(\frac{TotalMinutes}{MinutesPerOneMeet}=\) # of times they meet

\(\frac{40}{\frac{4}{9}}=40*\frac{9}{4}=90\) times that they meet

Answer D
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.
-- Albert Camus, "Return to Tipasa"

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: Two boys start cycling around a circular track in opposite directions [#permalink]

Show Tags

New post 12 Mar 2018, 10:08
rishabhmishra wrote:
Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?

A. 15
B. 30
C. 60
D. 90
E. 120


We can let t = the time they will meet for the first time:

10t + 5t = 400

15t = 400

t = 400/15 = 80/3 seconds

Since 40 minutes = 40 x 60 = 2,400 seconds, they will meet 2,400/(80/3) = (2,400 x 3)/80 = 30 x 3 = 90 times.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: Two boys start cycling around a circular track in opposite directions   [#permalink] 12 Mar 2018, 10:08
Print view
First unread post
Display posts from previous: Sort by

Two boys start cycling around a circular track in opposite directions

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

Moderators: chetan2u, VeritasPrepKarishma, niks18, mikemcgarry, Bunuel, generis

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions