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On a road, three consecutive traffic lights change after

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On a road, three consecutive traffic lights change after

by VJesus12 » Thu Jun 14, 2018 1:16 am

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On a road, three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously?

(A) 9 : 08 : 04
(B) 9 : 08 : 24
(C) 9 : 08 : 44
(D) 9 : 08 : 14
(E) 9 : 08 : 54

The OA is the option B.

I don't know how to get the correct answer in a fast way. Could anyone give me a good way to solve it? Thanks.
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by Vincen » Thu Jun 14, 2018 2:27 am
Hello Vjesus12.

We know that the three lights are switched on for the first time (and at the same time) at 9:00 A.M and they change each 36, 42 and 72 seconds respectively.

We have to find the time when they all change simultaneously. To find this time, we have to find the least common multiple of 36, 42 and 72, because this will be the first time when they change simultaneously after the 9:00 A.M.

Now $$36=2\cdot2\cdot3\cdot3=2^2\cdot3^2$$ $$42=2\cdot3\cdot7$$ $$72=2\cdot2\cdot2\cdot3\cdot3=2^3\cdot3^2.$$ Now, the least common multiple is $$LCM\left(36,\ 42,\ 72\right)=2^3\cdot3^2\cdot7=8\cdot9\cdot7=504.$$ Therefore, after 504 seconds all three ligths will change simultaneously.

Now $$504\ \text{secs}\ =\ 480\text{ secs}\ +\ 24\text{ secs}=\ 8\ \min\ +\ 24\ \text{secs} \ . $$ Therefore, the three ligths will change simultaneously for the first time at 9: 08 : 24 A.M.

This implies that the correct answer is the option B.

I really hope it is clear enough. <i class="em em-wink"></i>
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by swerve » Thu Jun 14, 2018 10:50 am
Hi Vjesus12!

Only B (504 sec) and E (534 sec) are divisible by 6
Only B is divisible by 6 and 7
9:08:24

Hence B is the correct answer.

Regards!
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by [email protected] » Thu Jun 14, 2018 5:36 pm
Hi All,

We're told that three consecutive traffic lights change after 36, 42 and 72 seconds respectively and that the lights are first switched on at 9:00 A.M. We're asked at what time the three will change simultaneously. This question has a couple of great 'shortcuts' built into it that you can use to avoid a lot of lengthy calculations.

To start, 12 seconds = 1/5 of a minute, so 72 seconds is exactly 1 1/5 minutes. Thus, any MULTIPLE of that length of time will also be in 'fifths.' This means that the correct answer must be some 'fifth' of a minute - and there are only 5 of those: 0 seconds, 12 seconds, 24 seconds, 36 seconds and 48 seconds. There's only one answer that fits that pattern...

Final Answer: B

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Contact Rich at [email protected]
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by Jeff@TargetTestPrep » Sun Jun 17, 2018 7:09 pm
VJesus12 wrote:On a road, three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously?

(A) 9 : 08 : 04
(B) 9 : 08 : 24
(C) 9 : 08 : 44
(D) 9 : 08 : 14
(E) 9 : 08 : 54
We are given that three consecutive traffic lights change after 36, 42, and 72 seconds, respectively. To determine at what time they will change simultaneously, we need to determine the least common multiple of 36, 42, and 72. Let's first break each number into prime factors:

36 = 9 x 4 = 3^2 x 2^2

42 = 6 x 7 = 2^1 x 3^1 x 7^1

72 = 9 x 8 = 3^2 x 2^3

To determine the LCM, we multiply the unique prime factors along with their respective largest exponent.

Thus, the LCM of 36, 42, and 72 = 2^3 x 3^2 x 7^1 = 504.

Let's now convert 504 seconds into minutes and seconds:

504 seconds = 504/60 minutes = 8 24/60 minutes = 8 minutes and 24 seconds

Since the lights are first switched on at 9 a.m., they will simultaneously change at 9:08:24 a.m.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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