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12 Days of Christmas GMAT Competition 2025 - Day 1: At 10:00 p.m.

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ankitksingh

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15 Dec 2025, 11:08

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This is a basic time speed distance problem, you just need to know d=s/t
d= 10
s= 1/3 m/min (3min per mile which means 1/3min per min)
t=0

at 10:48pm, he must travel some distance(lets say x) and be back at home
this means he travel in total d: x+x+10
s= 1/3 m/min (3min per mile which means 1/3min per min)
t = 48min

Hence: (2x+10)/48=1/3 or x=3

Fictional

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15 Dec 2025, 11:14

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The cyclist is 10 miles away from home at 10:00 and he is cycling at 3 miles/min so it will take him 30 mins to reach home. Therefore , reducing 30 mins from 10:48 will leave 18 mins .

The time the cyclist can ride far away from home is 3 miles which will take 9 mins and then he will travel back 9 mins to cover the same distance(that's how 18 mins will be complete) and then 30 mins to reach home at 10:48.

zindahi

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Bunuel

At 10:00 p.m., a cyclist is 10 miles from home on a straight road. From that time on, the cyclist continues riding farther from home at a constant speed of 3 minutes per mile, then turns around and rides back toward home at the same speed along the same road. If the cyclist must arrive back home at 10:48 p.m., how many additional miles can the cyclist travel away from home after 10:00 p.m. before turning around?

A. 2
B. 3
C. 6
D. 9
E. 12

Total Time to be taken from Point A (10 Miles Away from Home) to travel further straight away and Back Home = 48 Minutes

Let the Distance covered from Point A in a straight path until the U-turn is taken be D Miles.

As, Distance = Rate x Time,

The given rate is 3 Minutes per Mile, which can be written as 1/3 Miles per Minute
Hence,

10+2D = 1/3 x 48
2D = 16-10
D = 6/2 = 3

Hence, from Point A starting at 10:00 pm, the cyclist can go 3 Miles away and then take a U-turn to reach home at 10:48 pm.

sriharsha4444

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15 Dec 2025, 11:20

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At 3 minutes per mile, to cover the 10 miles distance back to home, it would take $3 * 10 = 30$ mins.
So left over $48-30 =18$ mins.

Since it takes the same to go and come back, cyclist has only 9 mins to reach then end before turning around.

At 3 minutes per mile, in 9 mins, cyclist will cover 3 miles before turning around

Ans: option B

Rishi705

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15 Dec 2025, 11:30

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The key inference to make is he will take 30 of the 48 mins to cover the 10miles from his starting point.
and since he is cycling at a constant speed is remaining 18 minutes will be split in 2
18/2=9 mins to cycle away.
speed 3mins for a mile.
So 3 miles away.

Bunuel

haldersujoy

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15 Dec 2025, 11:31

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Given,
Speed of the cyclist: 3 min. per mile.
The cyclist travelled from 10:00 p.m. to 10:48 p.m.
Therefore, total traveled time: 48 min.
Total distance covered 48/3 = 16 miles.
Now, let the extra distance that the cyclist covered from home be x miles.
going forward and returning home, the total distance will be 2x miles.
Therefore, 10+2x = 16
-> x = 3.
OA: B

Bunuel

AviNFC

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15 Dec 2025, 11:31

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Total 48 min available.
Now to cover d 10 miles to home 3*10 = 30 min gone
Remaining 18 min, 9 of which in 1 direction.
So 9/3 = 3 miles

Ans B

VidhiAgarwal1097

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15 Dec 2025, 11:39

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Total distance covered (to and from) post 10pm: 48mins/3min per mile = 16 miles
Additional miles = 16-10 = 6
Additional miles after 10pm before turning around = 6/2 = 3

Bunuel

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15 Dec 2025, 11:55

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Bunuel

Assume he covers x miles after 10pm before turning back and covered another x miles on his way back plus the initial 10 miles To complete the 10 miles at 3 minutes per mile the rider will take 30 minutes meaning he is left with (48-30) minutes to cover 2x miles which translates into 9 minutes for x miles at 3 minutes per mile.
So x =9minutes/3minutes per mile= 3 miles
Ans B

remdelectus

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15 Dec 2025, 11:57

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start time 10 pm
end time 10.48pm
Total time available =48 min
Start position: 10 miles from home
Speed: 3 min/miles
time=distance x rate(minutes/mile)
3x+3(10+x)=48
3x+30+3x=48
6x+30=48
6x=48-30
6x=18
x=3

suntincidunt

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15 Dec 2025, 11:59

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B. 3. 48/3=16...this is split into 3+13

Bunuel

martina3750

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15 Dec 2025, 12:04

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Total riding time = 48 minutes
Riding Miles = (48/3) = 16 miles
Already rided miles = 10 miles
-> Total Miles = 26 miles , so the riding time (one way) is (26/2) = 13 miles.

If he already ride 10 miles, he must ride 3 more before returning.

Answer B

Bunuel

canopyinthecity

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15 Dec 2025, 12:14

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The cyclist is 10 miles away from home. His speed is 3 minutes per mile. He started at 10 pm and needs to reach by 10:48 pm. Therefore, he has 48 minutes.
To return from his current position, he needs 30 minutes (10 miles * 3 minutes per mile)

This leaves him with 18 minutes for going ahead. Since he has to come back as well, one way time available is 9 minutes.

In 9 minutes, he can cover only additional 3 more miles. Hence (B) is the answer.

Dereno

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15 Dec 2025, 12:21

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Bunuel

Let us consider a line segment AB, where A denotes the home , and B denotes the Cyclist.

The distance AB is 10 miles at 10.00 pm.

The Cyclist rides at the same speed of 1 mile per 3 minutes.

The cyclist rides away from the home, and then turns back towards home. The cyclist reaches Home at 10:48 pm.

The distance the cyclist travels after 10:00 pm in the forward direction is d miles.

The distance the cyclist travels in the backward direction is : 10+d miles.

Total distance travelled after 10 pm = d + 10 + d = 10 + 2d miles.

Speed of cyclist is 1 mile per 3 mins.

By UNITARY METHOD : So, in 48 mins, the distance travelled is 48/3 miles = 16 miles.

10 + 2d = 16

2d = 6

d =3 miles.

The distance the cyclist travels after 10:00 pm before turning back = 3 miles.

Option B

eumdolore

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15 Dec 2025, 12:35

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Answer: B.3 miles. The cyclist can ride a total of (48min/3 min/miles)=16 miles. He will drive for x miles further from home and x+10 miles back home, so a total of 2x+10. From the equation 2x+10=16, results that x=3 miles.

Bunuel

Nitish03

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15 Dec 2025, 12:57

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Distance from home is 10 miles.
Speed is constant at 3 mins per mile(Given)
If cyclist arrive home at 10:48 i.e. 48 mins , total distance covered by cyclist after 10pm is
48 mins/3 miles per minute = 16 miles.
So additional distance covered by cyclist is 16 -10 = 6 miles.
Hence , additional miles traveled away from home before turning around = 6/2 =3 miles
Hence , option B

Noise1st

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15 Dec 2025, 13:17

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1. Divide 48 minutes by 3 minutes/mile. You'll get 16 miles
2. By 10:00 PM, the cyclist is already 10 miles away
3. So, he can go 3 miles further because he has just 16 miles left. 3 miles going and 13 miles returning

addictoread

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15 Dec 2025, 13:34

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Bunuel

Firstly, we need to find the speed :
In 3 mins, cyclist is travelling 1 mile. Therefore, in 1 min he will travel = 1/3 miles
Speed = Distance / Time = (1/3) / 1 = 1/3 miles/min

Now, let the distance travelled by cyclist after travelling 10 miles be x miles.

Total distance travelled after 10 pm = x + (10+x) miles
Total time = 48 mins

Therefore, speed = distance /time
=> 1/3 = (x+(10+x)) / 48
=> x = 3 miles

krati1712

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15 Dec 2025, 13:49

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Speed = 3 min per mile = (1/3) mile/min
If x miles travelled away from home after 10 pm, then total distance travelled from 10 pm to 10:48 pm = 2*x + 10 = speed *time = (1/3) miles/min * 48 min = 16 miles
Solving for x, we have x = 3

Bunuel