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Sarah and Alice both work at an auto shop, where they are responsible

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Joined: 02 Sep 2009
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Sarah and Alice both work at an auto shop, where they are responsible [#permalink]

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13 Sep 2017, 23:17
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Sarah and Alice both work at an auto shop, where they are responsible for changing the oil in cars. It takes Sarah 12 minutes to do one oil change, while it takes Alice only 10 minutes. If there are lots of cars that need their oil changed, and Sarah and Alice both start doing oil changes at exactly 9:00 A.M., and start the next car as soon as they finish changing the oil in another car, what is the first possible time that they will finish changing the oil of a car simultaneously?

A) 10:00 A.M.
B) 10:42 A.M.
C) 12:00 A.M.
D) 1:00 P.M.
E) 2:00 P.M.
[Reveal] Spoiler: OA

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Re: Sarah and Alice both work at an auto shop, where they are responsible [#permalink]

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13 Sep 2017, 23:22
Bunuel wrote:
Sarah and Alice both work at an auto shop, where they are responsible for changing the oil in cars. It takes Sarah 12 minutes to do one oil change, while it takes Alice only 10 minutes. If there are lots of cars that need their oil changed, and Sarah and Alice both start doing oil changes at exactly 9:00 A.M., and start the next car as soon as they finish changing the oil in another car, what is the first possible time that they will finish changing the oil of a car simultaneously?

A) 10:00 A.M.
B) 10:42 A.M.
C) 12:00 A.M.
D) 1:00 P.M.
E) 2:00 P.M.

LCM of 12 and 10 is 60
hence 9:00 AM + 60 mins = 10:00 AM (S would have completed 5 cars and A would have completed 6 cars)

A
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Re: Sarah and Alice both work at an auto shop, where they are responsible [#permalink]

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18 Sep 2017, 05:48
Bunuel wrote:
Sarah and Alice both work at an auto shop, where they are responsible for changing the oil in cars. It takes Sarah 12 minutes to do one oil change, while it takes Alice only 10 minutes. If there are lots of cars that need their oil changed, and Sarah and Alice both start doing oil changes at exactly 9:00 A.M., and start the next car as soon as they finish changing the oil in another car, what is the first possible time that they will finish changing the oil of a car simultaneously?

A) 10:00 A.M.
B) 10:42 A.M.
C) 12:00 A.M.
D) 1:00 P.M.
E) 2:00 P.M.

After starting together at 9:00 a.m., they will finish changing times simultaneously exactly after the least common multiple (LCM) of the number of minutes it takes for each of them to perform one oil change. Since 10 = 5 x 2 and 12 = 3 x 2 x 2, the LCM of 10 and 12 is 5 x 3 x 2 x 2 = 60. Therefore, they will finish together exactly 60 minutes after starting at 9:00 a.m., at which time it will be 10:00 a.m.

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Re: Sarah and Alice both work at an auto shop, where they are responsible   [#permalink] 18 Sep 2017, 05:48
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