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

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YashKakade

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15 Dec 2025, 09:24

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Consider that the cyclist travels an extra of x miles over the already travelled 10 miles before turning back.

At 10 pm, he is 10 miles away from his home. At 10:48 pm, he has returned back to his home after travelling an additional of x miles away from home before turning back.

So he has travelled [x miles (away from home) + x miles (turned and travelled towards home) + 10 miles (towards home)] in 48 minutes.

His speed is given as 3 minutes per mile i.e. he covers 1 mile in 3 minutes i.e. he covers (1/3) mile in a minute. So effectively his speed is 1/3 miles per minute.

So he has covered (2x + 10) miles in 48 minutes at a speed of 1/3 miles per minute.
Therefore, x = 3 miles.

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15 Dec 2025, 09:25

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since the distance is already 10 miles away from home at 10 PM and he needs to reach home at 10:48 PM. speed is 3 minutes per mile. by trial and error if he travels 3 miles from 10 PM onwards he has travelled 13 miles till 10:09 PM post that if he turns back to home, he will reach home in 13x3=39 minutes ie.. at 10:48 PM answer is 3 miles

rickyric395

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15 Dec 2025, 09:25

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Let x be the distance cyclist travel away from home, then total distance traveled = 10 + x
He has to travel back the same distance, then total distance traveled will be 20 + 2x
Given speed of cyclist = 1 mile in 3 min = 1/3 (mile/min)
Using speed = distance/time
time to come back is 48 min.
Putting all this in equation mentioned = 1/3 = 20 + 2x/48.
x = 2

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15 Dec 2025, 09:26

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in 48 mins go forward and return.
assuming x extra mile went forward and x miles would have to return.
therefore total: 2x miles + 10 miles(initial distance) within 48 mins with speed of 1/3 miles/min
48 = (2x + 10)/(1/3) => 16 = 10 + 2x => x = 3
additional miles cyclist can travel away from home is 3

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15 Dec 2025, 09:27

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Deconstructing the Question
Start Time: 10:00 p.m
End Time 10;48 p.m
Total Time Available: $48$ minutes
Rate (Speed): $3$ minutes per mile
Current Position: 10 miles from home .

Target: Find $x$, the additional miles traveled away from home beffore turning around.

Step 1: Calculate Total Distance Capacity
Since the cyclist travels at 3 minutes per mile, the total distance he can cover in 48 minutes is:
$\text{Total distance} = \frac{\text{Total Time}}{\text{Rate}}$
$\text{Total Distance} = \frac{48}{3} =16$ miles.

Step 2: Set up the Distance Equation
THe cyclist's Path consists of two parts:
1. Riding $x$ miles away from the starting point.
2. Riding back home from the turning point.
-The distance back to home is the sum of the additional miles ($x$) and initial distance from home (10 miles) .
-Return Distance = [m}x + 10[/m]

Total Path Lenght = (Distance Out) + (Distance Back)
$16 = x + (x + 10)$
$16 =2x + 10$

Step 3: Solve for x
$6 = 2x$
$x = 3$

The Cyclist can travel 3 additional Miles Away.

Answer: B

Brindac2

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15 Dec 2025, 09:28

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The easiest method to solve this is to try from the answer choices..
I started with middle value 6 miles. (c)

(C) Total distance covered = 16+6 = 22 miles;
Which should take 66 minutes at 3mph speed. Eliminate

Since the total time taken is 48 minues.. the option containing less than 6 would be next choice.

(B) Total distance covered = 13+3 = 16 miles; which should take 16*3 =48 minutes. Here we go.

B is the correct answer

sitrem

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15 Dec 2025, 09:31

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If he takes 3 minutes for each mile, we know he must take 30 minutes (10 miles for 3 minute per mile) to ride back home from the point he's at at 10PM.
This leaves him 48-30=18 minutes to go even further from home and come back.
We must divide this time by 2 since he must go AND come back, so he has 18/2 = 9 minutes to go travel further away from home. In 9 minutes he can travel 3 miles = 9 minutes / 3 minutes per mile.

So the answer is B. 3

givemethescore

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15 Dec 2025, 09:32

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From 10:00 to 10:48, the time that the cyclist went at 3 minutes per mile is 48 minutes
=> the total distance is: 48/3 = 16 miles

The route is illustrate as below with S is the distance we need to find
=> 10 + 2S = 16
=> S= 3

Attachments

IMG_5276.pdf [384.1 KiB]
Downloaded 14 times

Harika2024

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15 Dec 2025, 09:34

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Given
Total time = 48 min( diff between 10 pm and 10:48 pm)
Rate = 3 mins per mile , which can written as 1/3 mile per min
Formula => distance = rate * time
we can consider, distance = (1/3 mile per min) * (48 min) = 16 mile

We can observe from question that, we have distance as combination of 'Away from house' and 'towards house'
total distance = Away from house distance + towards house distance
16 = x + (10 +x)
16 = 10 + 2x
6 = 2x
3 = x

Therefore, cyclist can travel additional distance of 3 miles before turning around.

Note : During 'Away from house' segment -> cyclist is away from house by 10 miles and travels away x additional miles
During 'Towards house' segment -> cyclist travels x additional miles and 10 miles to house

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15 Dec 2025, 09:34

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The Answer will be B 3. Why? I'll Explain....Take it step by step....

Step 1. Cyclist is already 10 miles away, so the the minimum the cyclist has to travel back is 10 miles...Speed is 3 minutes per mile (BE CAREFUL ITS NOT 3 MILES PER MINUTE)....so for 10 Miles, the cyclist will take minimum 30 Minutes.....but this distance is not to be added in the answer..why? because its ADDITIONAL MILES BEFORE TURNING BACK ....
Have to reach home by 10:48 means the cyclist has only 18 mins for distance beyond 10 Miles on EACH SIDE or EACH WAY....

Step 2. Now that 18 mins has to be divided between two parts...One going ahead and one coming back....So 9 Minutes Each..... so the cyclist has only 9 minutes to travel further before turning back....this means...the cyclist can travel a maximum of 3 miles (3 MINUTES PER MILE is the speed ) ....So Answer is B....

Have tried to make a diagram....You have to calculate the part in yellow.. (The turning around distance is 0 as its the same path)

10 Miles. Cyclist
H-------------------|------------
O |
M-------------------|------------
E

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

GMAT2025champ

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15 Dec 2025, 09:36

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I finally got 3, but at first was using the typical t=d/s formula to no avail (=time wasted). I wonder how you automatically know to solve it otherwise, and not the usual way

Ak20047

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15 Dec 2025, 09:37

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Cyclist (C) is standing at Point X which is 10 miles away from home. From Pt. X to home, @ 3mins/mile, C will need 10*3 = 30 mins to reach home. He starts at 10 pm, needs to be back by 10.48pm, and takes 30 mins to reach home, hence he has 48-30 = 18 mins at his disposal.

he can use these 18 mins to travel further, turn and come back to Pt. X. Logically, the cyclist will travel the same distance further from Pt. X and return to it, and hence will take the same time in both the journeys. Therefore, dividing 18 by 2 gives us 9 mins, ie, he has 9 mins to travel further. 9 mins at 3 mins/mile will give 3 miles travelled (9/3=3).

Hence cylist can travel 3 additional miles before turning around and reaching home at precisely 10:48 pm.

Bunuel

arnab24

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15 Dec 2025, 09:37

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Given Cyclist is 10 miles away from home at 10:00 PM and by 10:48 PM he needs to come back to home. Speed of cyclist is 1 mile for every 3 mins. So in 48 mins , he will travel 16 miles. Now 16 miles will be equal to (Addtional distance + Additional distance + 10 ) miles. so from here Additonal distance that the cyclist travel away from home after 10:00 PM before turning around comes out to be 3 miles.

Bunuel

fugaquasi

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15 Dec 2025, 09:38

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Must return by 10:48 means must cover total distance (fixed 10 plus variable) in 48 mins:

distance = 10+x miles
speed = 3 minutes per meter => 1/3 miles per minute or 1/180 miles per second

simple from here:

s=d/t
1/180= (10+x)/(48*60)

=> 16=10+x
=> x=6

6 extras miles

vasu1104

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15 Dec 2025, 09:39

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rate = 1/3 miles/min
say distance after 10 pm- x miles traveled before turning back.
so total traveled back to home= 2x+10
rate= 1/3 miles/ min
time= 48 min

2x+10= 16
2x= 6
x=3

Bunuel

vikramadityaa

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15 Dec 2025, 09:40

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Bunuel

Using Option:

A) 2 - 2 miles * 3 minutes per mile = 6 min. (10:06)
Total time taken to cover the distance back home = 12*3 = 36
36+6 = 42 (10:42) - Times doesn't add up.
B) 3 - 3 miles * 3 minutes per mile = 9 min. (10:09)
Total time taken to cover the distance back home = 13*3 = 39
39+9 = 48 (10:48) - time match.
The same follows for all other options.

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15 Dec 2025, 09:43

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Bunuel

Firstly, the total time available for the trip is from 10:00 PM to 10:48 PM which is 48 minutes. And, the cyclist's speed is constant at 3 min/mile which is equivalent to a speed s = [1][/3] miles/min.

If we let 'd' be the additional distance that the cyclist travels away from the home after reaching the 10 mile mark. Then, distance travelled away from home is d miles and the distance travelled back to home is 10+d miles.

The total distance 'D' travelled after 10:00 PM is:
D= d+ (10+d) = 10+2d miles.

Alternatively the total distance= speed x time
D = s x t
= 1/3 * 48 miles
= 16 miles

Then, 10+2d = 16 that is, d= 3.

Thus, the additional distance that the cyclist can travel is 3 miles.

ToniSeb

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15 Dec 2025, 09:47

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Since the cyclist spends 3 minutes for 1 mile. The time the cyclist in 30 minutes goes 10 miles.

As the cyclist is 10 miles away from home at 10:00 pm. He has a total of 48 mins to get back home and will cover the 10 miles in 30 minute.

So the extra time left with him is 48-30 = 18 minutes.
This 18 minute will be divided into two as the cyclist moves to and fro. So 9 mins to go ahead and 9 mins back home.

The cyclist takes 3 mins for 1 mile so in 9 min the cyclist will travel 3 miles, which is the extra distance.

meenumaria

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15 Dec 2025, 09:49

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IMO B 3 is the answer
10miles 10pm
home ------------->-------| x miles away and back each total 2x
total distance to travel in 48mins 2x+10 miles
and given : 1 mile 3 mins
->10miles- 30 mins
Remaining 18 mins convert to miles so 6 miles so 2x=6
x=3
total distance further from hosue is 3 miles

HarishChaitanya

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15 Dec 2025, 09:50

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step 1:

convert speed of cyclist into miles per hour from minutes per miles, i.e, 3mintues per mile will be 20 miles per hour in this case

step 2:

For 48 min, calculate distance travelled by cyclist by using speed from step 1, d= (48/60)*20, equals to 16miles,

step 3:

from the 16 miles cycilist travelled in 48 mins, 10 miles is the distance he had covered which was the distance he was away from home at 10:00 pm

therefore the additional distance is 6 miles that he travelled of which 3 miles is the distance which he travels before turning around

so the answer is B. 3miles

Bunuel