GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 May 2020, 22:39

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

In a race of 4800 meters run on a circular track of 400 meters length

  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: 64216
In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 06 Jan 2020, 07:07
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

50% (01:58) correct 50% (02:17) wrong based on 30 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 358
Location: United States
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 07 Jan 2020, 02:54
1
Bunuel wrote:
In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?

A. 4
B. 5
C. 6
D. 7
E. 8


Explanation:

Let the slower athlete speed be 3m/min, the faster = 5m/min

The faster athlete overtakes the slower for first time after 400/2 = 200min i.e. when it has covered 1000 meters. After every 200 minutes Faster athlete will overtake slower athlete

Now the total time taken by Faster athlete to cover entire race = 4800/5 = 960 mins

Hence total no of times he will overtake = 960/200 = 4.8 i.e 4 times

IMO-A
Manager
Manager
avatar
B
Joined: 30 Jun 2019
Posts: 209
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 07 Jan 2020, 14:42
These questions are a little confusing because i'm not sure what points are supposed to be considered significant.
Does the very start count as a data point? What about the end? Since one guy finishes first, does he "meet" with the other guy after every lap thereafter?

The answer is either 4 (the number of times the faster runner laps the slower runner during the race)
1000M:600M
2000M:1200M
3000M:1800M
4000M:2400M
Or every 2.5 laps:1.5 laps

5 times if you count just the start as significant. 6 if you count just the final end as significant.
I believe they meet 10 times if you count every lap after the first runner finishes as significant, and that's not an answer choice.
Intern
Intern
avatar
B
Joined: 25 Nov 2019
Posts: 10
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 07 Jan 2020, 22:07
Bunuel wrote:
In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?

A. 4
B. 5
C. 6
D. 7
E. 8


Let's start by calculating the time through relative speed formula : Relative speed = Relative distance / time
So, here the relative speed is (2) {the difference between ratio of the speed of the two athletes}
Thus, 2=400/T
T=400/2 = 200 mins

Now, we calculate how much distance will the faster athlete cover in 200 mins => 200 * 5 = 1000 mtrs.

since, it will take 1000 mtrs for the faster athlete to cross the other one in a 4800 mtr race. It becomes quite clear that there will be total of 4 points each after the faster athelete run 1000 mtrs.

The correct ans is option A.
Intern
Intern
avatar
B
Joined: 30 Nov 2019
Posts: 19
Location: Lebanon
GMAT 1: 670 Q46 V36
CAT Tests
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 08 Jan 2020, 01:37
\(Formula: S = \frac{D }{ T}\)

\(\frac{S1}{S2}=\frac{3}{5}\) --> S1 = 3k and S2 = 5k (k >0)

D2 = D1 + n x 400 (n>0) Since S2 > S1, there is no way that they can meet within the 1st lap.

When the 2 will meet, the time will be the same --> T1 = T2 --> \(\frac{D1 }{ S1} = \frac{D2 }{ S2}\) or D1 x S2 = D2 x S1

D1 x 5k = (D1 + 400n) x 3k
5 x D1 = 3 x D1 + 1200n
2 x D1 = 1200n

D1=600n
D2=1000n

for n=5, D2=5000 > 4800. So 0 < n < 5 --> They meet 4 times

Answer is A

Hope it helps!
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10590
Location: United States (CA)
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 09 Jan 2020, 11:15
Bunuel wrote:
In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?

A. 4
B. 5
C. 6
D. 7
E. 8

We can let the speed of the faster person = 10 and that of the slower person = 6. Notice that the faster person will finish the race in 4800/10 = 480 seconds.

The faster person must overtake the slower person when he runs exactly 1 lap, 2 laps, etc. more than the slower person. Let t be the time it takes when the faster person overtake the slower person We can create the equations:

10t = 6t + 400 (for 1 lap), 10t = 6t + 800 (for 2 laps), etc.

Notice that none of the values of t can be more than 480 seconds, the time when the faster person finishes his race. Solving the first equation, we have:

4t = 400

t = 100

That is, it takes 100 seconds for the faster person to overtake the slower person by 1 lap.

Solving the second equation, we have:

4t = 800

t = 200

That is, it takes 200 seconds for the faster person to overtake the slower person by 2 laps.

We can see that the values of t are increasing by 100, so it will take 300 seconds for the faster person to overtake the slower person by 3 laps, 400 seconds by 4 laps. Since the next one will be 500 seconds and recall that t can’t be more than 480, then there are only 4 times when the faster person overtakes the slower person.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64216
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 10 Jan 2020, 03:03
CEO
CEO
User avatar
V
Joined: 03 Jun 2019
Posts: 2899
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Premium Member Reviews Badge CAT Tests
Re: In a race of 4800 meters run on a circular track of 400 meters length  [#permalink]

Show Tags

New post 31 Mar 2020, 10:42
Bunuel wrote:
In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?

A. 4
B. 5
C. 6
D. 7
E. 8


Given: In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5.

Asked: If they run in the same direction, how many times do they meet in the entire race?

400 m * 12 laps = 4800 m

Let the speeds be 3x & 5x respectively

When they meet each time
400 = 2x * T
T = 200/x

Time to complete the race = 4800/5x = 960/x

Times they meet = (960/x) / (200/x) = 4.8 ~ 4 times ; Since time they meet should be an integer

IMO A
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
GMAT Club Bot
Re: In a race of 4800 meters run on a circular track of 400 meters length   [#permalink] 31 Mar 2020, 10:42

In a race of 4800 meters run on a circular track of 400 meters length

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





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