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705-805 (Hard)|   Algebra|   Word Problems|         
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 01:22
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The number of kilometers walked in a month is the number of people * the number of people because km per person = the number of participants. Setting n for number of people you get n^2.

For months 1-3 every one is active so km = 3n^2

months 4-9 only half are active so 6(n/2)^2 = 1.5n^2

Months 10-12 1/4 active so: 3* (n/4)^2

3n^2 + 1.5n^2 + 3/16n^2 = (75/16)n^2 = 10,800 km so n^2 =2304 and n =48. The answer is E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 01:38
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So from the passage the equation we can make is
3(x*x) + 6(x/2*x/2) + 3(x/4*x/4) = 10800
Solving this
48x^2 + 24x^2 + 3x^2= 10800 * 16
x^2 = 10800 * 16 / 75
x^2 = 144 * 16
x = 48
Answer 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


 


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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 01:57
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Ans Choice E : Let no. of participants at start of challenge = x ;
Given Distance travelled by each participant = no of active participant that month ; Dist travelled for 1-3 months = 3 * x^2
No. of participants from 4-9 months = x/2 ; Dist travelled for 4-9 months = 6 *(x/2)^2
No. of participants from 10-12 months = x/4 ; Dist travelled for 10-12months = 3*(x/4)^2
Total distance travelled = 3x^2 + 3x^2/2 + 3x^2/16 = 10800 ; upon solving , 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


 


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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 04:06
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Let, total participants at beginning = 16x

Months.........Active Participants......Each Walks........Total Distance
1-3 ......................... 16x ......................... 16x Km ............. 3(16x)(16x)= 768x^2
4-9 ......................... 8x ........................... 8x Km .............. 6(8x)(8x)= 384x^2
10-12 ...................... 4x ........................... 4x Km ............ 3(4x)(4x)= 48x^2

Total distance = 10,800
768x^2 +384x^2 +48x^2 =10800
1200 x^2 =10800
x^2 =10800/1200=9
x=3

Total participants at beginning =16x =16*3=48

E. 48
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 04:28
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Assume the total number of participants is x
If each member walks x miles then total miles for the three months = 3x(x)x(x)= 3x^2
Month 3 to 9 will be (1/2x)x(1/2x)x6=6/4x^2
Month 9 to 12 (1/4x)x(1/4x)x3= 3/16x^2
Total = 3x^2+6/4x^2+3/16x^2= 75/16x^2=10800
x^2=2304
x=48
Ans 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


 


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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 04:43
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10,800=N^2(3+6/4+3/16)=N^2 (48+24+3/16)=N^2*75/16=10,800*16/75=2304, then root of 2304 is 48. Hence E is our answer.
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 05:05
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Requirement:
# of km per month = # of people
Total km per month = # of people * # of km = x^2
Eg: 40 people join, 40 km/person => total km/month = 40*40 = 1600 km

So, if we break it down as equation we divide into 3 sections
with x= # of people

1. Month 1-3

3-month * x * x = 3x^2

2. Month 4-9 (after 6 months, half of the remaining participants leave)

6-month * 1/2 x * 1/2 x = [3][/2]x^2

3. Month 9-12 (the last 3 months, half of the participants leave)

3-month * 1/4 x * 1/4x = [3][/16]x^2


So we have the equation

3x^2 + 3/2 x^2 + 3/16 x^2 = 10.800

= 75/16 x^2 = 10.800
= x^2 = 10.800 * 16 / 75

we got X = range between 40 and 50 -> so answer is E. 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


 


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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 05:31
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1st 3 MonthsNext 6 MonthsLast 3 Months
Participants: \(N\)Participants:\(\frac{N}{2}\)Participants: \(\frac{N}{4}\)
Distance per person:\(N\)Distance Per person: \(\frac{N}{2}\)Distance Per Person: \(\frac{N}{4}\)
Distance Total: \(3*(N^2)\)Distance Total: \(6*(\frac{N^2}{4})\)Distance Total: \(3*(\frac{N^2}{16})\)
\(Total Distance = 3*(N^2)+6*(\frac{N^2}{4})+3*(\frac{N^2}{16})=10,800 KM\)
Question asks for \("N"\)
\(\sqrt{N2}=\sqrt{2304}\)
\(N=48\)
ATTENTION: Distance per person is equal to number of participants as the questions states "each active participants records a distance equal to number of active participants"
IMO
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 05:49
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Let x be the number of participants at the beginning
As per the question, the total km walked by a participants in a given month = total number of members
Total distance walked by a group in a month = Number of particpants * Total distance per participant = x*x = x^2
a) For the first 3 months - Total distance = 3*x^2
b) For the next 6 months - remaining participants = x-1/2x = 1/2x
Hence total distance for next 3 months = 6*1/2x*1/2x = 3x^2/2
c) For the last 3 months -> Remaining participants = 1/2x*1/2 = 1/4x
Total distancefor the last 3 months = 3*1/4x*1/4x = 3x^2/16

Now it is given that total distance for the 12 months = 10800 Km
Accordingly, we get an equation -> 3x^2+ 3x^2/2 +3x^2/16 = 10800
75x^2/16 = 10800

Now I substituted the options as per question and got the answer x = 48
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 06:09
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Let there be x total participants in a yearlong challenge
Total distance travelled by them in 1 year = 10800km
x is divisble by 4 as given by the passage since half the participants leave twice in the year

Total distance travelled by a participant = x km
=> Total distance travelled by all the participants in a month = x^2
=> Total distance travelled by all the participants in the first 3 months = 3x^2

Half the people leave
Participants left = x/2
Total distance travelled in the next 6 months = 6* (x/2)*(x/2) = (3x^2) / 2

Again half the people leave and 3 more months left

Participants left = x/4
Total distance travelled in the last 3 months = 3**x/4)*(x/4) = (3x^2) / 16

=> Total distance travelled = 3x^2 + (3x^2)/2 + (3x^2)/16 = 10800
=> 75x^2 = 172800
=> x = 48

E. 48
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 06:19
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the logic is straightforward.
Number of people active (who walk and record) = Number of kilometers walked by each person.
So total number of km = (# of people active)^2

We have also been given that for the first 3 months, all were active
Then 6 middle months - 1/2 of the initial number was active
And finally last 3 months, 1/2*1/2*the initial number was active.

I did the trial and error method and since the number was on the higher side, I considered 40 first and then 48.
With 40 I got:
(40*40*3) (number of months)
+ (20*20*6)
+ (10*10*3)
= 7,500
A number lower than this anyway won't work. So the answer should be 48

Testing 48
(48*48*3)
+ (24*24*6)
+ (12*12*3)
= 10,800

Answer is E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 06:28
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Word problems boil down to forming the right equation.
So if there are k active participants in a month & each walks k km - then total grp distance = k*k = k square

Months 1 to 3 with n active participants = 3n square
months 4 to 6 - n/2 so monthly n square by 4
over 6 months 6* n square /4 = 3 nsquare /4
10 to 12 months n/4 whole squared
Over 3 months = 3n square /16

EQn = 3 n square + 3 n square/2 + 3 nsquare/16 = 10800
Gives n = root 2304
Thus n = 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


 


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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 06:54
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x friends

3 months: 3*x^2
6 months: 6*(x/2)^2 = (6/4)*x^2 = (3/2)*x^2
3 last months: 3*(x/4)^2 = (3/16)*x^2

3*x^2 + (3/2)*x^2 + (3/16)*x^2 = 10800
(3 + 3/2 + 3/16)*x^2 = 10800
(48 + 24 + 3)/16 * x^2 = 10800
75/16 * x^2 = 10800
x = 48

IMO E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 07:04
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IMO : E
Active partivipation = n
each = n
total = n^2
for 3 months =3. n^2

month 4-9 ===>
n/2 . n/2 = n^2/ 4
for 6 months ==> 6. n^2/ 4
10-12 months
N^2/16 ---> for 3 months 3. n^2/16

total distance = 75n^2/16 = 10800
n = 48
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 07:14
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N: number of participants at the beginning

In the first 3 months: N^2 + N^2 + N^2 = 3N^2
In the next 6 months: (N/2)^2 + (N/2)^2 + (N/2)^2 + (N/2)^2 + (N/2)^2 + (N/2)^2 = 6N^2/4 = 3N^2/2
In the next 12-9=3 months: (N/4)^2 + (N/4)^2 + (N/4)^2 = 3N^2/16

Adding all:
(3+3/2+3/16)N^2 = 75N^2/16 = 10800

N^2 = 10800*16/75 = 108*100*16/75 = 36*100*16/25 = 36*4*16
N = 6*2*4 = 48

Answer E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 07:24
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Checking posting just a test if it’s working
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 07:30
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p number of friends

3 months with p*p=p^2 km, so 3p^2 km
6 months with (p/2)*(p/2) km, so 6p^2/4 = 3p^2/2
the year has 12 months, so (p/2)/2=p/4 frinds continue walking another 3 months: 3*(p/4)*(p/4) = 3p^2/16

total = 3p^2 * (1+1/2+1/16) = 3p^2 * (25/16) = 10800
p^2 * (25/16) = 3600
p^2 = 3600*16/25
p = 60*4/5 = 12*4 = 48

The answer is E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 07:45
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X number of friends

3 months X friends walking X km -> 3X^2
6 months X/2 friends walking X/2 km -> 3X^2/2
3 months X/4 friends walking X/4 km -> 3X^2/16

3X^2 + 3X^2/2 + 3X^2/16 = 10800
X^2 + X^2/2 + X^2/16 = 3600
25X^2/16 = 3600
X = sqrt(3600*16/25) = 6*10*4/5 = 48

The correct answer is E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 08:53
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Let n be 6the number of people in the group at the beginning.

After 3 months 1/2 left = > n/2, After 6 months 1/2 of remaining left => N/4
Distance recorded by each person = number of people remaining in group

So for first 3 months, distance recorded = N*N *3months = 3N^2
For next 6 months = (N/2)*(n/2) * 6months = 3N^2/2
For the last 3 months of the year = (N/4)(N/4)*3 = 3N^/16

Total distance recorded for the group = 10800

3N^2 + 3N^2/2 + 3N^2/16) = 10800

Solving for N we get N = 48


Answer E
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GMAT Club World Cup 2026 (Day 9): At the beginning of a yearlong 17 Jul 2026, 09:19
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ANS is E.
Actually the way question is written is very confusing after 3 4 time read I get what it mean to say maybe my personal comprehension issue but at last I was able to get the answer.
so it says same # of people to same kms so say in the beginning x people in a grp so each will walk also x.

so eqn would be 3x^2 + 3x^2/2 + 3x^2/16 = 10800 => solving gives us x =48 So ANS is E

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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


 


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