12 Days of Christmas GMAT Competition 2025 - Day 7: In a confrontation

Reon

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24 Dec 2025, 02:15

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Each Jedi can destroy 10 droids per minute.
At the end of each minute, four Jedi retreat and are replaced by four Padawans, each of whom can destroy half as many droids as a Jedi per minute. Each Padawans destroy 5 droids per minute.
Total droids destroyed= 720

First minute
J= 12 and P=0
Number of droids destroyed= 12*10= 120
At end, 4J retreat and 4P join

Second minute
J=8 and P=4
Number of droids destroyed = 8*10 +4*5 = 80+20 = 100
At end, 4J retreat and 4P join again

Third minute,
J=4 and P=8
Number of droids destroyed= 4*10 + 8*5 = 40+40 = 80
At end, 4P retreat and 4P join again
At end of this we now only have 12 P destroying the droids.

Total droids destroyed till now = 120+100+80 = 300
Remaining droids to be destroyed by P alone = 720-300 = 420

Time 12 P will take to destroy remaining droids alone = 420/12*5 = 420/60 = 7 minutes

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24 Dec 2025, 02:23

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Haha, is it fandom day today? I don't know too much about Star Wars, but May the Force Be With Me as I try to get this one right

The Jedis are stronger, capable of destroying 10 droids per minute. There are 12 Jedis. In the first minute, they will destroy 120 droids.

But once the first minute ends, 4 of the 12 Jedis retreated, leaving 8 behind, and 4 Padawans - capable of destroying 5 droids per minute - take their place. That's another 8*10 + 4*5 = 100 droids destroyed. 220 done. 500 to go.

When the second minute ends, 4 of the remaining 8 Jedis retreat, leaving 4 Jedis behind, and 4 Padawans join their 4 counterparts to take the Padawan count up to 8. That's another 4*10 + 8*5 = 80 droids destroyed. 420 to go.

When the third minute ends, the remaining Jedis retreat too, leaving no Jedi behind, and 4 Padawans join their 8 counterparts and now all 12 fight the droids alone. That's another 12*5 or 60 droids destroyed 360 to go.

Now, first thing first - the first minute of the Padawans fighting alone, has passed already, taking 60 droids with them. 360 remain - and we now know each minute'll have the Padawans destroying 60 droids by themselves. That's another 360/60 = 6 minutes of action. Add it to the first minute, the answer is D, 7 minutes.

Bunuel

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24 Dec 2025, 02:44

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Answer is 7 mins

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24 Dec 2025, 02:58

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Bunuel

We have 12 Jedi and their destroying rate is 10 droid per min

and Padawans destroying rate is 5 droid per min

Now every min 4 jedi replaced by padawans and question is how many minute do padawans have to fight alone after last jedi retreated

Let's calculate together how many droid they destroy

1 min -12 * 10 = 120
2 min - 8 * 10 + 4 * 5 = 100 (4 jedi replaced)
3 min - 4 * 10 + 8 * 5 = 80
Ok after 3 min all jedi are replaced and till now total 300 droids are destroyed

so

12 * 5 * x = 420 ( remaining droid)

x = 7 min

Our answer is D

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24 Dec 2025, 02:58

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Below table shows the #droids destroyed every min. (#droids destroyed by Jedi and padawan are 10/min and 5/min resp)

Time	#Jedi	#Padawan	#droids destroyed
At t = 0	12	0	0
At t = 1	8	4	12 * 10 = 120
At t = 2	4	8	120 + 8 * 10 + 4 * 5 = 220
At t = 3	0	12	220 + 4 * 10 + 8 * 5 = 300
At t = 4	0	12	300 + 12 * 5 = 360 and so on

From t = 3 onwards, we get an AP with d = 60. Thus,

720 = 300 + (n - 1) * 60
=> n = 8

The battle took place till t = 10 (3 + 8 - 1) min. Thus, the padawans fought alone for 7 min.

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24 Dec 2025, 03:40

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In a confrontation with battle droids, twelve Jedi engage in combat. Each Jedi can destroy 10 droids per minute. At the end of each minute, four Jedi retreat and are replaced by four Padawans, each of whom can destroy half as many droids as a Jedi per minute. After the last four Jedi retreat, the Padawans continue fighting the droids alone. At the end of the confrontation, a total of 720 battle droids are destroyed. Throughout the confrontation, all Jedi and Padawans fight at their full rates, with none incapacitated. How many minutes did the Padawans fight alone after the last Jedi retreated?

A. 3
B. 3.5
C. 6
D. 7
E. 10

1st Minutes ------> droids destroyed by 12 Jedi = 120

2nd Minute --------> droids destroyed by 8 Jedi and 4 Padawans = 8*10 +4*5 = 100

3rd Minute ----------> droids destroyed by 4 jedi and 8 Padawans = 4*10+8 *5= 80

Post 3 minutes 720- 300 = 420 droids are left to be destroyed and 12 Padawans have to destroy the same -- time taken = 420/(12*5) = 70/10 = 7 minutes Answer D.

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24 Dec 2025, 04:04

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Destructions by minutes
min 1. 12 jedi, 10 droids/min each: 12X10 120 droids
min 2. 4 jedi -4 padawans to be 8 jedi & 4 padawans
(8X10)+(4X5)=80+20=100 droids
min 3. 4 more jedi replaced = 4 jedi 8 padawans
(4X10)+(8X5)=80 droids
after min 3. 4 jedi retreat=12 padawans alone
12X5=60 droids/min
let y=min padawans fought alone
120+100+80+60y=720
300+60y=720
60y=420
60y/60=420/60
y=7

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24 Dec 2025, 04:07

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Min 1 = 12 Jedi
Damaged= 12x 10= 120 droids

Min 2 = 8 Jedi & 4 padawans
Damage= 8x10+4x5=100

Min 3 = 4 Jedi & 8 Padawans
Damage= 4x10+8x5=80

Min 4= 12 padawans (all Jedi gone)
12x5=60
Total before all pad fight alone is first 3 minutes
= 120+100+80= 300
Remaining droids is 720-300= 420
Padawans to fight alone : Rate is 12x5=60d/m
Time needed= 420/60 = 7

Answer is 7 minutes

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24 Dec 2025, 04:21

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Let's write the balance equation of destroyed droids:

12*10 (end 1st minute) + 8*10 + 4*5 (end 2nd minute) + 4*10 + 8*5 (end 3rd minute) + 12*5*X (minutes left) = 720

we get 60*X = 420 ==> X = 7 min

IMO D!

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24 Dec 2025, 05:27

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Relative speeds of Jedi and Padawans are: $j=10$ and $p=0.5j=5$
Therefore, while Jedi were in the fight, they managed to destroy that many droids over the first couple of minutes:

Minute 1: $12j=120$

Minute 2: $8j+4p=80+20=100$

Minute 3: $4j+8p=40+40=80$

And from the fourth minute, only Padawans were left with the speed of $12p=60$ droids/minutue.

The army left for padawans to destroy was therefore $720-120-100-80=420$, and with the speed of 60 per minute, they needed $t_{solo}=420/60 = 7 $ minutes.
Therefore, the answer is D.

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24 Dec 2025, 05:51

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As 4 jedis leave and 4 Padawans join every minute, the first time there will be no jedis would be in minute 4 (12 jedis total).
Also, rate with which jedis destroy droids = 10/min, for padawans it will be 5/min (half of jedis). Lets assume they fought for T mins after jedis are gone. Then:
=> Total droids destroyed = 12*10 + (8*10+4*5)+(4*10+8*5)+ (12*5*t) = 750 => t= 7 mins. Answer = D

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24 Dec 2025, 06:18

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Lets take this problem Minute by Minute:

Given
Jedi rate: 10 droids/min
Padawan rate: half of a Jedi = 5 droids/min
Start: 12 Jedi
Every minute: 4
Jedi leave and 4 Padawans enter
Total droids destroyed = 720

Step 1: Lets compute destruction during mixed fighting
Minute 1: 12 Jedi
Destruction = 12 × 10 = 120 12×10=120
Minute 2 : 8 Jedi + 4 Padawans
Destruction = 8 × 10 + 4 × 5 = 80 + 20 = 100

Minute 3: 4 Jedi + 8 Padawans
Destruction = 4 × 10 + 8 × 5 = 40 + 40 = 80 4×10+8×5=40+40=80
So far total destruction is of 300 minutes.

Step 2: Padawans fight alone
After minute 3: 12 Padawans
Destruction rate = 12×5=60 droids/min
Remaining droids: 720 − 300 = 420
Time required: 420/60 = 7 minutes

Ans D.

Bunuel

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24 Dec 2025, 06:39

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The correct answer is D. Jedi rate = 10 droid/min ; Padawan rate = 5 droid/min
Min 1
12 jedi * 10 (rate) = 120 droid ; 720 -120 = 600 remaining
Min 2
(8 jedi * 10 )+ (4 padawan * 5(rate)) = 100; 500 remaining
Min 3
(4 *10) + (8 * 5) = 80; 420 remaining
Min 4
12 * 5 = 60 ; 360 remaining
From minute 4 padawans are fighting alone and every minute only 60 droids will be destroyed therefore 360 / 60 = 6 minutes
Thus 6 + 1(4th minute is when they start fighting alone) = 7 minutes

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24 Dec 2025, 06:49

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let J = 10 droids/min and p = 5 droids/min
acc. to ques post every minute:
12j 8j+4p 4j+8p 12p*n(minutes) = 720
120 + 100 + 80 + 60n = 720 => n = 7

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24 Dec 2025, 07:06

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We know that,

Jedi = 10 droids/min
Padawan = 5 droids/min

Min 1:
12 Jedi
Rate = 12*10 = 120 droids/min
Total = 120 droids

Min 2:
8 Jedi + 4 Padawan
Rate = 8*10 + 4*5 = 100
Total = 120 + 100 = 220

Min 3:
4 Jedi + 8 Padawan
Rate = 4*10 + 8*5 = 80
Total = 80 + 220 = 300

Min 4 and later
12 Padawan
Rate = 12*5 = 60

We need to know how much time Padawans fought alone to reach the total 720 droids destroyed count

=> Remaining = 720 - 300 = 420

Time = 420 / 60 = 7 mins

D. 7

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24 Dec 2025, 07:12

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Each Jedi destroys 10 droids/min.
Each Padawan destroys 5 droids/min.

Minute 1: 12 Jedi
Rate = 12*10 = 120

Minute 2: 8 Jedi + 4 Padawans
Rate = 8*10+4*5 = 80+20 =100

Min 3: 4 Jedi + 8 Padawan
Rate = 4*10 + 8*5 = 80

Total after 3 minutes = 120+100+80 = 300

After last Jedi retreat, 12 Padawans only:
Rate = 12*5 = 60
Total droids destroyed = 720
Remaining after 3 minutes: 720 -300 = 420

Time for padawans aline: 420/60 = 7 mins

Bunuel

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24 Dec 2025, 07:14

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Bunuel