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# Train A leaves a station every 16 minutes and Train B leaves every 19

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Joined: 02 Sep 2009
Posts: 56304
Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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02 Nov 2016, 02:55
00:00

Difficulty:

5% (low)

Question Stats:

83% (01:06) correct 17% (01:46) wrong based on 111 sessions

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Train A leaves a station every 16 minutes and Train B leaves every 19 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 608 minutes
B. 304 minutes
C. 190 minutes
D. 70 minutes
E. 35 minutes

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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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02 Nov 2016, 03:05
Bunuel wrote:
Train A leaves a station every 16 minutes and Train B leaves every 19 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 608 minutes
B. 304 minutes
C. 190 minutes
D. 70 minutes
E. 35 minutes

IMO B
The next moment when both the trains would leave simultaneously would be 16*19= 304 minutes after the 1st instance.
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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02 Nov 2016, 07:57
Bunuel wrote:
Train A leaves a station every 16 minutes and Train B leaves every 19 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 608 minutes
B. 304 minutes
C. 190 minutes
D. 70 minutes
E. 35 minutes

LCM of 19 and 16 is 304.
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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02 Nov 2016, 09:01
1
Bunuel wrote:
Train A leaves a station every 16 minutes and Train B leaves every 19 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 608 minutes
B. 304 minutes
C. 190 minutes
D. 70 minutes
E. 35 minutes

Quote:
both trains just left the station simultaneously, how long until they do so again

So, we need to find the LCM and as 16 & 19 have no common factor in them (CO Prime Set) , LCM = 16*19 = 304

Hence, answer will be (B) 304
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Joined: 21 Apr 2016
Posts: 165
Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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02 Nov 2016, 18:19
LCM of 16 and 19 = 304
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Joined: 02 Oct 2016
Posts: 4
Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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03 Nov 2016, 00:06
We have to find the LCM:

19 is a prime number which means the LCM of 16 and 19 has to be 16*19=304

Correct answer is B.
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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04 Nov 2016, 09:39
Bunuel wrote:
Train A leaves a station every 16 minutes and Train B leaves every 19 minutes. If both trains just left the station simultaneously, how long until they do so again?

A. 608 minutes
B. 304 minutes
C. 190 minutes
D. 70 minutes
E. 35 minutes

The LCM can be used to determine when two processes that occur at differing rates or times will coincide. Since we are given that Train A leaves a station every 16 minutes and Train B leaves every 19 minutes, we need to determine the LCM of 16 and 19. Since 16 and 19 have no common factors other than 1, we can determine the LCM of 16 and 19 to be the product of the two numbers; that is, the trains will again leave the station at the same time in 16 x 19 = 304 minutes.

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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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21 Nov 2016, 13:45
Can somebody explain the intuition of this question please?
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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21 Nov 2016, 13:45
Can somebody explain the intuition of this question please?
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19  [#permalink]

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22 Aug 2018, 16:08
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Re: Train A leaves a station every 16 minutes and Train B leaves every 19   [#permalink] 22 Aug 2018, 16:08
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# Train A leaves a station every 16 minutes and Train B leaves every 19

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