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12 Jan 2026, 10:52
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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
A. 3
B. 3.5
C. 6
D. 7
E. 10
12 Jan 2026, 10:52
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Official Solution:
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
In the first minute, 12 Jedi destroy 120 droids.
In the second minute, 8 Jedi destroy 80 droids and 4 Padawans destroy 20 droids, for a total of 100 droids.
In the third minute, 4 Jedi destroy 40 droids and 8 Padawans destroy 40 droids, for a total of 80 droids.
So, before the last Jedi retreats, 120 + 100 + 80 = 300 droids have been destroyed.
With a total of 720 droids destroyed, the Padawans destroy 720 - 300 = 420 droids after the last Jedi retreats.
Since the 12 Padawans destroy 12 * 5 = 60 droids per minute, it takes them 420/60 = 7 minutes to destroy the remaining droids.
Answer: D
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
In the first minute, 12 Jedi destroy 120 droids.
In the second minute, 8 Jedi destroy 80 droids and 4 Padawans destroy 20 droids, for a total of 100 droids.
In the third minute, 4 Jedi destroy 40 droids and 8 Padawans destroy 40 droids, for a total of 80 droids.
So, before the last Jedi retreats, 120 + 100 + 80 = 300 droids have been destroyed.
With a total of 720 droids destroyed, the Padawans destroy 720 - 300 = 420 droids after the last Jedi retreats.
Since the 12 Padawans destroy 12 * 5 = 60 droids per minute, it takes them 420/60 = 7 minutes to destroy the remaining droids.
Answer: D
