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The Baton Rouge bound bus leaves a station every 16 minutes and the Ak

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The Baton Rouge bound bus leaves a station every 16 minutes and the Ak  [#permalink]

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New post 10 Dec 2016, 05:18
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Question Stats:

78% (01:10) correct 22% (01:12) wrong based on 119 sessions

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The Baton Rouge bound bus leaves a station every 16 minutes and the Akron bound bus leaves every 18 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 288 minutes
B. 144 minutes
C. 72 minutes
D. 42 minutes
E. 34 minutes

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Re: The Baton Rouge bound bus leaves a station every 16 minutes and the Ak  [#permalink]

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New post 10 Dec 2016, 11:19
Bunuel wrote:
The Baton Rouge bound bus leaves a station every 16 minutes and the Akron bound bus leaves every 18 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 288 minutes
B. 144 minutes
C. 72 minutes
D. 42 minutes
E. 34 minutes


LCM ( 16, 18 ) = 144

Hence, correct answer will be (B) 144
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Re: The Baton Rouge bound bus leaves a station every 16 minutes and the Ak  [#permalink]

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New post 14 Feb 2017, 10:54
Abhishek009 wrote:
Bunuel wrote:
The Baton Rouge bound bus leaves a station every 16 minutes and the Akron bound bus leaves every 18 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 288 minutes
B. 144 minutes
C. 72 minutes
D. 42 minutes
E. 34 minutes


LCM ( 16, 18 ) = 144

Hence, correct answer will be (B) 144



Hi Abhishek009,

I am not sure of LCM (16, 18) being equal to 144. Am I missing something?.

16x = 18y

prime factors of 16 ---->(2^4) and prime factors of 18 --->(3^2 *2),

so for the two sides of the equation (16x = 18y) to be equal, x has to be at the least 9 (i.e., 3^2), and y has to be at least 8 (i.e., 2^3).

16x = 18y ----> 16*9 = 18 * 8 or 2^4 * 3^2 = 3^2 * 2 *2^3 ===> 144

Answer: B
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Re: The Baton Rouge bound bus leaves a station every 16 minutes and the Ak  [#permalink]

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New post 02 Oct 2018, 18:22
Bunuel wrote:
The Baton Rouge bound bus leaves a station every 16 minutes and the Akron bound bus leaves every 18 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 288 minutes
B. 144 minutes
C. 72 minutes
D. 42 minutes
E. 34 minutes


To determine when the buses will leave the station simultaneously again, we need to determine the least common multiple (LCM) of 16 and 18.

16 = 2^4

18 = 3^2 x 2^1

The LCM is 3^2 x 2^4 = 9 x 16 = 144. Thus, it will be 144 minutes until the Baton Rouge-bound and Akron-bound buses again leave the station simultaneously.

Answer: B
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Re: The Baton Rouge bound bus leaves a station every 16 minutes and the Ak  [#permalink]

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New post 03 Oct 2018, 00:45
Bunuel wrote:
The Baton Rouge bound bus leaves a station every 16 minutes and the Akron bound bus leaves every 18 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 288 minutes
B. 144 minutes
C. 72 minutes
D. 42 minutes
E. 34 minutes


The trains will leave after a time that is common multiple of 16 and 18

Least common multiple of 16 and 18 = 144

i.e. both trains will leave station together again after 144 minutes

Answer: Option B
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Re: The Baton Rouge bound bus leaves a station every 16 minutes and the Ak &nbs [#permalink] 03 Oct 2018, 00:45
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