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16 Jul 2026, 08:00
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E
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Difficulty:
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74% (02:27) correct
26%
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wrong
based on 212
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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
A. 12
B. 24
C. 30
D. 40
E. 48
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M46-48
16 Jul 2026, 09:00
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GMAT Club Official Solution:
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
Let n be the number of participants at the beginning.
For the first 3 months, there are n active participants, and each records n kilometers per month.
Total for the first 3 months:
3 * n * n = 3n^2
After the first 3 months, half of the participants leave, so n/2 participants remain.
For the next 6 months, each of the n/2 active participants records n/2 kilometers per month.
Total for the next 6 months:
6 * n/2 * n/2 = 3n^2/2
After the next 6 months, half of the remaining participants leave, so n/4 participants remain.
For the final 3 months, each of the n/4 active participants records n/4 kilometers per month.
Total for the final 3 months:
3 * n/4 * n/4 = 3n^2/16
Thus:
3n^2 + 3n^2/2 + 3n^2/16 = 10,800
48n^2/16 + 24n^2/16 + 3n^2/16 = 10,800
75n^2/16 = 10,800
n^2 = 10,800 * 16/75
n^2 = 2,304
n = 48
Answer: E.
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
Let n be the number of participants at the beginning.
For the first 3 months, there are n active participants, and each records n kilometers per month.
Total for the first 3 months:
3 * n * n = 3n^2
After the first 3 months, half of the participants leave, so n/2 participants remain.
For the next 6 months, each of the n/2 active participants records n/2 kilometers per month.
Total for the next 6 months:
6 * n/2 * n/2 = 3n^2/2
After the next 6 months, half of the remaining participants leave, so n/4 participants remain.
For the final 3 months, each of the n/4 active participants records n/4 kilometers per month.
Total for the final 3 months:
3 * n/4 * n/4 = 3n^2/16
Thus:
3n^2 + 3n^2/2 + 3n^2/16 = 10,800
48n^2/16 + 24n^2/16 + 3n^2/16 = 10,800
75n^2/16 = 10,800
n^2 = 10,800 * 16/75
n^2 = 2,304
n = 48
Answer: E.
General Discussion
16 Jul 2026, 08:17
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Let x be the number of participants at the start of the challenge.
Hence for the first 3 months, each participant will record x number of kms. Thus, x participants will record x*x = x^2 kms every month. Thus, total steps recorded in the first 3 months = 3*x^2
Half of the original participants drop out at this point. Thus the new number of participants is x/2
For the next six months these x/2 participants walk x/2 kms each every month.
Thus, total no. of kms in the next six months = (x/2)*(x/2)*6 = 6x^2/4 = 3x^2/2
At this point, half of the remaining participants drop out again. Thus new number of participants = (1/2)*(x/2) = x/4
Thus, total no. of kms in the last 3 months = (x/4)*(x/4)*3 = 3x^2/16
Now the total no. of kms walked by the group throughout the year = 10800
Thus,
3x^2 + 3x^2/2 + 3x^2/16 = (48x^2+24x^2+3x^2)/16 = 75x^2/16 = 10800
Thus, x^2 = 10800*16/75 = 144*16
Therefore, x = 12*4 = 48
Thus, answer is E
Hence for the first 3 months, each participant will record x number of kms. Thus, x participants will record x*x = x^2 kms every month. Thus, total steps recorded in the first 3 months = 3*x^2
Half of the original participants drop out at this point. Thus the new number of participants is x/2
For the next six months these x/2 participants walk x/2 kms each every month.
Thus, total no. of kms in the next six months = (x/2)*(x/2)*6 = 6x^2/4 = 3x^2/2
At this point, half of the remaining participants drop out again. Thus new number of participants = (1/2)*(x/2) = x/4
Thus, total no. of kms in the last 3 months = (x/4)*(x/4)*3 = 3x^2/16
Now the total no. of kms walked by the group throughout the year = 10800
Thus,
3x^2 + 3x^2/2 + 3x^2/16 = (48x^2+24x^2+3x^2)/16 = 75x^2/16 = 10800
Thus, x^2 = 10800*16/75 = 144*16
Therefore, x = 12*4 = 48
Thus, answer is E
16 Jul 2026, 08:23
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Take total no of participants as x
given- every particiapnt walks km equal to total active participants
so for first 3 months
total distance = x^2
for next 6 months
total participant = x/2
so distance = x/2 x x/2 = x^2 /4
and multiply by 6 for 6 months = 3x^2/2
For last 3 months
particiapnts = x/4
so distance = (x/4)^2 x 3 = 3x^2/16
Adding all
3x^2 + 3x^2/2 + 3x^2/16 = 10800
3x^2 (1 + 1/2 +1/16) =10800
3x^2 x 25/16= 10800
x^2 = 10800x16 / 25x3
x^2 = 2304
x= 48
So E in answer
given- every particiapnt walks km equal to total active participants
so for first 3 months
total distance = x^2
for next 6 months
total participant = x/2
so distance = x/2 x x/2 = x^2 /4
and multiply by 6 for 6 months = 3x^2/2
For last 3 months
particiapnts = x/4
so distance = (x/4)^2 x 3 = 3x^2/16
Adding all
3x^2 + 3x^2/2 + 3x^2/16 = 10800
3x^2 (1 + 1/2 +1/16) =10800
3x^2 x 25/16= 10800
x^2 = 10800x16 / 25x3
x^2 = 2304
x= 48
So E in answer
