Last visit was: 06 Sep 2026, 02:28 It is currently 06 Sep 2026, 02:28
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
   1   2   3   4   5   
705-805 (Hard)|   Algebra|   Word Problems|         
User avatar
Maesha
User avatar
Joined: 11 Jun 2026
Last visit: 31 Jul 2026
Posts: 29
Own Kudos:
25
 [1]
Given Kudos: 4
Concentration: Leadership, Economics
Schools: HBS '26 (S)
Schools: HBS '26 (S)
Posts: 29
Kudos: 25
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 09:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
X people X/2 people X/4 people
[----------------][----------------------------][-----------------]
1st 3 month 4-9th month last 3 month = total 12 month

suppose , X number of people participated . per day each ran X km . so in one month , total run is = X^2 km
after 3 month , total distance covered = 3X^2 km



after 3 month , half left , remaining X/2 . in one month total run = X^4 km
so total run in the span of 4th to 9th month = 6X^2/4 km


after 6 month , another half left , remaining X/4 , one month each covered X^2/16 km
so total run in the last 3 month = 3X^2/16 km


now ,
3X^2 + 6X^4 +3x^2/16 =10800

or , 48x^2 +24x^2+ 3x^2 = 10800. 16

or , X^2 = 10800.16/75

or , x =2304 ^0.5

or, x =48


So , total number of participants in the begining were 48.
User avatar
Theeldertwin
User avatar
Joined: 28 Dec 2025
Last visit: 05 Sep 2026
Posts: 163
Own Kudos:
32
 [1]
Given Kudos: 88
Concentration: Strategy
Schools: HEC Sept '27 INSEAD Aug '27 NUS '27
GMAT Focus 1: 655 Q84 V84 DI79
Schools: HEC Sept '27 INSEAD Aug '27 NUS '27
GMAT Focus 1: 655 Q84 V84 DI79
Posts: 163
Kudos: 32
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 09:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's assume there were x active participants at the start. For the first 3 months, they walked for x km each. So total distance in first 3 months = 3*x*x = 3x^2

Next, half of them drop off. So we are left with x/2 participants. These would each walk for x/2 km each for 6 months. So total in the next 6 months = 6*(x/2)*(x/2) = 6(x^2)/4 = 3(x^2)/2

For the next 3 months, half of the rest further drop off. So we are left with x/4 active participants who would walk for x/4 km each. This gives us a total of 3*(x/4)*(x/4) = 3(x^2)/16 km

Thus, total distance = 3x^2 + 3x^2/2 + 3x^2/16 = (48+24+3)x^2/16 = 75x^2/16

75x^2/16=10800

On solving, we get x=48
Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
User avatar
MANASH94
User avatar
Joined: 25 Jun 2025
Last visit: 05 Sep 2026
Posts: 165
Own Kudos:
121
 [1]
Given Kudos: 27
Location: India
Schools: IIM IIM ISB
GMAT Focus 1: 525 Q80 V76 DI72
GPA: 2.9
Products:
GMAT Club Tests
Schools: IIM IIM ISB
GMAT Focus 1: 525 Q80 V76 DI72
Posts: 165
Kudos: 121
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 09:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let participants initially be n
in 3 months participants= 3n^2
6 Months participants = 6(n/2)^2 = 3n^2/2
last 3 months = 3 (n/4)^2 = 3n^2/16

3n^2 + 3n^2/2 + 3n^2/16 = 10800
n^2 = 2304
n = 48 (negative n is not possible).
Ans is E.
Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
User avatar
ankushsambare
User avatar
Joined: 13 Jun 2022
Last visit: 05 Sep 2026
Posts: 313
Own Kudos:
225
 [1]
Given Kudos: 230
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
Products:
GMAT Club Tests Forum Quiz
Schools: ISB '27 Wharton '26 INSEAD Aug '26
Posts: 313
Kudos: 225
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 09:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let initial no of participants be n
first 3 months: n, each walk n km/month
total = 3n^2
next 6 months n/2 participants, each walk n /2 km/months
total = 6 (n/2)^2
= 3/2 n^2
Last 3 months n/4 participants, each walks n/4 km/month
total = 3 (n/4)^2
= 3/16*(n^2)

Total distance: 3n^2 + 3/2 n^2 + 3/16^2 = 10800
75/16 n^2 = 10800
n^2 = 10800 *16/75 = 2304
n = 48
Option : E
User avatar
Nkathiyawadi
User avatar
Joined: 08 Feb 2026
Last visit: 01 Sep 2026
Posts: 57
Own Kudos:
29
 [1]
Given Kudos: 36
Location: India
Posts: 57
Kudos: 29
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
No. of participants initially = N

Kms run by each participants = no. of active participants in the group

During first 3 months, kms run : N*N * 3 months = 3N^2
During next 6 months, kms run : (N/2)^2*6 = 6*N^2/4 (because half of the participants leave after 3 months)
During next 3 months, kms run = (N/4)^2*3 = 3*N^2/16 (because half of the partipants leave after 6 months duration. For remaining time period of 12-3-6 =3 months)

Total kms run = 3N^2 + (6/4)N^2 + (3/16)N^2 = (75/16)N^2 = 10800

then N = sqrt(10800*16/75) = 48 = Option E

There were 48 participants initially.

Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
User avatar
abhishekb1352
User avatar
Joined: 16 Jan 2026
Last visit: 06 Sep 2026
Posts: 43
Own Kudos:
29
 [1]
Given Kudos: 26
Products:
Forum Quiz
Posts: 43
Kudos: 29
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let us assume the number of active participants at the beginning of the challenge was x.

For the first 3 months, x number of people each walked for x kms and hence the total distance recorded is 3.x.x = 3x^2
For the next six months, the number of active participants dropped by half and hence the total distance recorded for these 6 months are 6.(x/2).(x/2) = (3/2).x^2
For the last 3 months, the number of active participants have dropped to just x/4 and hence the total distance recorded is 3.(x/4).(x/4) = (3/16).x^2

Now it is given that the total distance for the year is 10,800 kms and hence adding up the above algebraic eqns to this total value given would look something like this
3x^2 + 3/2.x^2 + 3/16.x^2 = 10800
taking lcm on left side and then dividing the eqn by 3 we get
25/16 * x^2 = 3600

here after taking root of x, we can see that x = 48.

Hence answer is option E
User avatar
heyaa
User avatar
Joined: 19 Dec 2024
Last visit: 05 Sep 2026
Posts: 71
Own Kudos:
60
 [1]
Given Kudos: 46
Location: India
Posts: 71
Kudos: 60
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
first 3 months = 3*n*n = 3n^2
next 6 months = 6*n/2*n/2 = 3/2 n^2
next 3 months = 3*n/4*n/4 = 3/16 n^2
total 3*(1+1/2+1/16)*n^2 = 10800
=> 3*25/16*n^2 = 10800
=> 25/16n^2 = 3600, sq rt on both sides
=> 5/4*n = 60; n = 48.
User avatar
okHedwig
User avatar
Joined: 13 Apr 2022
Last visit: 01 Sep 2026
Posts: 106
Own Kudos:
66
 [1]
Given Kudos: 70
Posts: 106
Kudos: 66
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO E

Let no of participants at beginning be x
then
As per Q, x.x.3 + (x/2).(x/2).6 + (x/4).(x/4).3 = 10800
solving for x, we get x^2 = 10800 . 16/ 75 = 36 . 4. 16
or x = 6. 2. 4 = 48
Hope this helps
Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
User avatar
FlushLoop
User avatar
Joined: 05 Jul 2026
Last visit: 06 Aug 2026
Posts: 62
Own Kudos:
57
 [1]
Posts: 62
Kudos: 57
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Number of participants = n

After 3 months = Kms = 3n^2

Next 6 months

Number of participants = n/2

Kms = 6(n/2)^2 = 3n^2/2

Last 3 months

Number of participants = n/4

Kms = 3(n/4)^2 = 3n^2/16

Total = 3n^2 + 3n^2/2 + 3n^2/16 = 10800

75n^2 = 172800

n^2 = 2304

n = 48

Option E
User avatar
GulfTube
User avatar
Joined: 13 Apr 2026
Last visit: 17 Aug 2026
Posts: 210
Own Kudos:
70
 [1]
Given Kudos: 77
Posts: 210
Kudos: 70
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:40
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let participants be x at start.

total distance first 3 months: each participant travels x km so total = 3*x^2
total distance month 4-9: participants left: x/2. total distance now traveled = 6*(x/2)(x/2) = 6*((x^2)/4)
total distance month 10-12: x/4 people are left. total distance now travelled = 3*(x/4)(x/4) = 3*(x^2/16)

overall distance = 3x^2 + (3/2)x^2 + (3/16)x^2 = (75/16)x^2 = 10800
x^2 = (10800*16)/75 = 144*16
x = √(144*16) = √144 * √16 = 12*4 = 48
E
User avatar
sonit1987
User avatar
Joined: 29 Jul 2025
Last visit: 30 Aug 2026
Posts: 61
Own Kudos:
51
 [1]
Location: India
Concentration: Operations, Sustainability
WE:Operations (Energy)
Posts: 61
Kudos: 51
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given:- 1)A group of people tracking the total distance travelled in a challenge.
2)Every month, each participants travel distance equal to number of active participants in that group
3) total distance travelled in a year is 10800 km
4) only active participant walk, rest stop walking and once any participant walk recorded, it will count towards group total walk

Lets assume at the beginning of challenge, there were x participants in total

First 3 months all participants walked, so individually each would have walked x Km/month. so one participant would have walked 3x km in 3 month.

x participant would have walked x*3x=3*(x^2) km in first 3 month. ( this is recorded for group)

Now, given half the participant left after 3 month, so now participant are x/2. and they all walked for next 6 months.

As per questions terms and conditions each remaining participant now would be walking x/2 km per month and in next 6 month each participant will walk 6*x/2=3x km
so x/2 participant will walk x/2*3x= 3/2*(x^2) km.( recorded)

After these 6 months another half left the group, so now remaining participant are x/4

remaining months in a year is 12-3-6=3 months

so for last 3 months each x/4 participants will walk 3*x/4*x/4= 3/16*(x^2) km( recorded)

Total Km travelled is 3*(x^2)+3/2*(x^2)+3/16*(x^2)= 75/16*(x^2)= 10800
x^2=10800*16/75= 2304
X=sqrt(2304)= 48

Answer-E(48)
User avatar
BongBideshini
User avatar
Joined: 25 May 2021
Last visit: 05 Sep 2026
Posts: 390
Own Kudos:
242
 [1]
Given Kudos: 137
Location: India
Concentration: Entrepreneurship, Marketing
Schools: HBS '27 Stanford '27 Wharton '27 Sloan '27
GPA: 3.8
WE:Engineering (Government)
Schools: HBS '27 Stanford '27 Wharton '27 Sloan '27
Posts: 390
Kudos: 242
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let's assume initially there were x participants.

\(\\
3x^2 + 6(x/2)^2 + 3(x/4)^2 = 10800\\
(75x^2)/16 = 10800\\
x=48\\
\)
User avatar
paragw
User avatar
Joined: 17 May 2024
Last visit: 05 Sep 2026
Posts: 385
Own Kudos:
389
 [1]
Given Kudos: 62
Products:
Forum Quiz
Posts: 385
Kudos: 389
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 10:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here's my solution for this question
Attachments

IMG_20260716_232125.jpg
IMG_20260716_232125.jpg [ 432.77 KiB | Viewed 103 times ]

User avatar
yashsharma1
User avatar
Joined: 18 Apr 2025
Last visit: 05 Sep 2026
Posts: 75
Own Kudos:
49
 [1]
Given Kudos: 26
Location: India
Schools: IESE '26 (WL)
GMAT Focus 1: 645 Q81 V82 DI83
Products:
GMAT Club Tests Forum Quiz
Schools: IESE '26 (WL)
GMAT Focus 1: 645 Q81 V82 DI83
Posts: 75
Kudos: 49
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:02
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we assume the number of participants at the beginning of the 12 months is 12x, then as per the attached photo, the total kms logged by all the participants during the whole year will be 675x^2

So, 675x^2 = 10800 and x = 4.
Then, the number of participants at the beginning of the challenge were 12(4) = 48
Attachments

Photo.png
Photo.png [ 10.08 KiB | Viewed 102 times ]

User avatar
remdelectus
User avatar
Joined: 01 Sep 2025
Last visit: 06 Sep 2026
Posts: 120
Own Kudos:
112
 [1]
Given Kudos: 6
Posts: 120
Kudos: 112
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let no. of participants at the beginning be-n
first 3 months
every participant=n km/m
Group total/m= n*n=n^2
3 months=3n^2

from month 4-9
half participants leave so n/2 remain
each walk n/2km/m
group total/m=n/2*n/2=n^2/4
6 months=6*n^2/4=3n^2/2

From month 10-12
1/2 of the rem participants leave, n/4 remaining
each walk n/4km/m
group total/m=n/4*n/4=n^2/16
3 months=3*n^2/16=3n^2/16
Total distance= {3n^2+(3n^2/2) +(3n^2/16) =10800} *16
48n^2+24n^2+3n^2=172800
75n^2=172800
75n^2/75=172800/75
n^2=2304
n=48
ANS: E. 48
User avatar
AviNFC
User avatar
Joined: 31 May 2023
Last visit: 09 Aug 2026
Posts: 365
Own Kudos:
421
 [1]
Given Kudos: 5
Posts: 365
Kudos: 421
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
let n people start
first 3 months:
each walks n .. so n^2 per month.. 3 months 3n^2
next 6 months
total walks=6*(n/2)^2
final 3 months
3*(n/4)^2

total= 3n^2 + 6n^2/4 + 3 n^2/16
=75n^2/16=10800
n=48

Ans E
User avatar
kingbucky
User avatar
Joined: 28 Jul 2023
Last visit: 05 Sep 2026
Posts: 649
Own Kudos:
745
 [1]
Given Kudos: 368
Location: India
Products:
My Reviews Forum Quiz
Posts: 649
Kudos: 745
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let \(x\) be the initial number of participants in the challenge.

According to the rules, if there are \(P\) active participants in a given month, each walks \(P\) kilometers. This means the group as a whole records \(P \times P = P^2\) kilometers for that month.

Let's break the yearlong (12-month) challenge into three distinct phases:

Phase 1 (First 3 months):
Number of participants = \(x\)
Distance per month = \(x^2\)
Total distance for this phase = \(3x^2\)

Phase 2 (Next 6 months):
Half the participants leave, leaving \(\frac{x}{2}\) active participants.
Distance per month = \((\frac{x}{2})^2 = \frac{x^2}{4}\)
Total distance for this phase = \(6 \times \frac{x^2}{4} = \frac{3x^2}{2}\)

Phase 3 (Final 3 months):
Half of the remaining participants leave, leaving \(\frac{x}{4}\) active participants.
Distance per month = \((\frac{x}{4})^2 = \frac{x^2}{16}\)
Total distance for this phase = \(3 \times \frac{x^2}{16} = \frac{3x^2}{16}\)

We are told the total distance recorded for the entire year is 10,800 km. We can set up our master equation by adding the distances from all three phases:
\(3x^2 + \frac{3x^2}{2} + \frac{3x^2}{16} = 10800\)

To solve this elegantly without multiplying large numbers, let's factor out \(3x^2\):
\(3x^2(1 + \frac{1}{2} + \frac{1}{16}) = 10800\)

Divide both sides by 3 and find a common denominator for the fraction:
\(x^2(\frac{16 + 8 + 1}{16}) = 3600\)
\(x^2(\frac{25}{16}) = 3600\)
\(x^2 = 3600 \times \frac{16}{25}\)

Since both 3600 and 16/25 are perfect squares, we can avoid large calculations by taking the square root of both sides right now:
\(x = \sqrt{3600} \times \sqrt{\frac{16}{25}}\)
\(x = 60 \times \frac{4}{5}\)
\(x = 12 \times 4\)
\(x = 48\)

There were 48 participants at the beginning of the challenge.

Correct Answer: E
User avatar
Vivek1707
User avatar
Joined: 22 May 2020
Last visit: 04 Sep 2026
Posts: 353
Own Kudos:
186
 [1]
Given Kudos: 150
Products:
GMAT Club Tests Forum Quiz
Posts: 353
Kudos: 186
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Let the number of walkers be 8x in the begining.

Since each walker ran the number of km equal to the number of participants. It means each of the 8x guy ran 8x km per month

Hence first 3 month - 64x^2 * 3 Km
Next 6 months - 4x*4x * 6
Last 3 months - 2x*2x * 3

Adding this up will give 10,800

4^x2*3 (16+8+1) = 10,800
12x^2*25 = 10,800
x = 6
Hence total number of people = 8 * 6 = 48 I ll go with E




Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
User avatar
Shlok02
User avatar
Joined: 08 Jan 2024
Last visit: 05 Sep 2026
Posts: 65
Own Kudos:
41
 [1]
Given Kudos: 6
Products:
GMAT Club Tests Forum Quiz
Posts: 65
Kudos: 41
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
Let participants = p
each participant records the same distance as the number of participants

for first 3 months,
total distance = p^2 * 3 = 3p^2

for next 6 months
remaining participants = p- p/2 = p/2
distance = 6 * (p/2)^2 = 3p^2/2

for last 3 months
remaining participants = p/2 - p/4 = p/4
total distance = 3 * (p/4)^2 = 3p^2/ 16

Total distance = p^2 + 3p^/2 + 3p^2/ 16 = 10800
75p^2 / 16 = 10800

p = sqrt (3600*16/25)
p = 48 (E)
User avatar
zitipiti
User avatar
Joined: 09 Jul 2026
Last visit: 05 Sep 2026
Posts: 82
Own Kudos:
3
 [1]
Given Kudos: 21
Location: India
Concentration: Finance, International Business
Schools: ESSEC HEC ESADE
GPA: 7
Products:
GMAT Club Tests
Schools: ESSEC HEC ESADE
Posts: 82
Kudos: 3
 [1]
GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 16 Jul 2026, 11:50
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
At the beginning of a yearlong walking challenge, a group of friends begins tracking the total distance walked by the group. In each month, every active participant walks and records a number of kilometers equal to the number of active participants in the challenge during that month. After the first 3 months, half of the participants leave the challenge, and after the next 6 months, half of the remaining participants leave. Any participant who leaves stops walking and recording distances for the challenge, but the distance that participant recorded earlier still counts toward the group’s total. If the group records a total of 10,800 kilometers during the year, how many participants were in the challenge at the beginning?

A. 12
B. 24
C. 30
D. 40
E. 48


 


This question was provided by GMAT Club
for the GMAT World Cup Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 


⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
Show more
let the total no. of participants be 16x
they walk 16x Km for 3 months
so total distance travelled in 3 months = (16x)(16x)*3
now half of them has left, we have 8x people and they travel for next 6 months
their total distance will be = (8x)(8x)*6
again half of 8x left, we are left with 4x people travelling for last 3 months of the year
their total distance will be = (4x)(4x)*3

summing up all the distances and equating it with 10800 which is given to us
3x^2(2^8 + 2*2^6 + 2^4) = 10800
on solving x = 3
total no. of participants = 16x = 48
   1   2   3   4   5   
Moderator:
Bunuel
Math Expert
113157 posts