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01 Dec 2014, 05:30
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:43) correct
28%
(02:56)
wrong
based on 156
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Tough and Tricky questions: Word Problems.
The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time all five colored lights will all flash together at the exact same time?
A) 0:03 AM
B) 0:04 AM
C) 0:06 AM
D) 0:12 AM
E) 0:24 AM
Kudos for a correct solution.
Source: Chili Hot GMAT
01 Dec 2014, 06:16
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Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
intheend14
01 Dec 2014, 18:41
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We must find the LCM by doing prime factorization.
20 = 2*2*5
30 = 2*3*5
45 = 3*3*5
60 = 2*2*3*5
80 = 2*2*2*2*5
To find the LCM, determine the most number of occurrences of every prime factor and multiply these together. For 2, 80 has 4 factors of 2. For 3, 45 has 2 factors of 3 and they all have one factor of 5. Let's multiply 4 factors of 2, 2 factors of 3 and a factor of 5:2^4*3^2*5 = 720 seconds or 12 minutes after we start. Choice D
20 = 2*2*5
30 = 2*3*5
45 = 3*3*5
60 = 2*2*3*5
80 = 2*2*2*2*5
To find the LCM, determine the most number of occurrences of every prime factor and multiply these together. For 2, 80 has 4 factors of 2. For 3, 45 has 2 factors of 3 and they all have one factor of 5. Let's multiply 4 factors of 2, 2 factors of 3 and a factor of 5:2^4*3^2*5 = 720 seconds or 12 minutes after we start. Choice D
