On a road, three consecutive traffic lights change after 36, 42 and 72

Question

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

GMATinsight · Answer

They will change simultaneously after a time which is a common multiple of 36, 42 and 72 seconds = LCM (36, 42 and 72 seconds) = 504 Seconds = 8 mins and 24 seconds

So the next time = 9:08:24

Answer: Option B

gracie · Answer

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

JeffTargetTestPrep · Answer

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 started at 9 a.m., they will simultaneously change at 9:08:24.

Answer: B

Rohn1003 · Answer

504 sec 
8 min 24 sec

Posted from my mobile device

Take the lcm and convert seconds to minutes

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

On a road, three consecutive traffic lights change after 36, 42 and 72

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

On a road, three consecutive traffic lights change after 36, 42 and 72

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards